Guerinot did not even realise she was British, and so made no attempt to contact the British Consulate.
'If we had got involved at an early stage, it could have changed the case completely,' says Paul Lynch, the British Consul-General in Houston. 'We would have ensured she got the best legal representation.'
Guerinot, however, has America's worst record as a capital punishment defender. He has begged juries to save the lives of 24 different clients, but 20 have been sentenced to death - more than the entire death row population of 25 states.
Under Texan law, it is juries, not judges, that decide whether to impose the death penalty. Ten of Guerinot's clients have already been executed, the most recent last November.
Yet no court has been willing so far to spare Carty's life, and she is only too well aware that she may meet the same fate.
'Yes, I do contemplate the fact I may be executed. I'm not going to tell you that I'm happy about having to face death for someone else's crime. But this is a matter I have no control over. If that day comes, I will get up in the morning and tell the Lord I'm ready to go.'
As part of my research, I tried to interview Guerinot but his office said he was uncontactable because he was taking a break from legal work in order to run a rodeo.
However, when I investigated this case three years ago, we did manage to talk, and he insisted that his lethal track record was not caused by his incompetence, but by the fact that Houston's judges assigned him the toughest, most gruesome cases.
'The easy ones, somehow, never came to me,' he said. He also betrayed an extraordinary attitude towards Carty, describing her as 'hedonistic and self-centred'.
He claimed the reason he didn't spend more time with her before the trial was that she was ' uncooperative' and had to be 'bribed' with a bar of chocolate to talk to him at all.
In fact, Carty suffers from a severe chocolate allergy - one bite would make her go into anaphylactic shock.
Linda Carty as a young woman
Carty is British by virtue of spending the first 23 years of her life on the West Indian island of St Kitts, which did not achieve independence from the Crown until 1983.
She still speaks with a distinctive Caribbean lilt, and the heroes of her youth were the invincible West Indies cricket team. 'We all thought of ourselves as extensions of the motherland, and that's what we were taught,' she says.
'We had to learn English history. It was part of our culture - Henry VIII, colonisation, Churchill.
'I sang for Prince Charles as a soloist with the choir when he came to my school. I curtsied and then it was like, "Oh my God, how am I going to get the words out, I'm actually in front of the Prince."'
Carty worked on St Kitts as a primary school teacher, and also gave birth to a daughter, Jovelle. In 1982, when Jovelle was two, Carty's parents decided to move the family to America.
Carty studied pharmacology at Houston University, but kept her British passport. 'My mum loves the Union Jack and she used to tell me, "Do not give up your British citizenship. If you can't have a dual nationality, do not give it up."
'The US Immigration and Nationality Service used to write to me every 18 months and say, "You need to naturalise." But I never did.'
It was while Carty was still a student that she began a highly dangerous part-time job as an undercover informant for the US Drug Enforcement Administration, infiltrating both Caribbean and Colombian mafias.
Her handler, Special Agent Charlie Mathis, swore in an affidavit filed for her appeals that she risked her life repeatedly, and over the years she was paid thousands of dollars.
He gave evidence briefly at her trial - but for the prosecution - to state that at the time of Carty's alleged crime, she was no longer on the DEA's 'books'.
The effect, says Carty's Supreme Court petition, was to create the impression that she could not be trusted.
But Guerinot never spoke to Mathis before the trial, and remained unaware of the evidence that, according to Mathis's later affidavit, he could have given - that Carty still often called him with tips, and that if one had led to an investigation, 'I would not have hesitated' to put her on the books again.
'I do not believe her to be a compulsive liar,' Mathis added. 'She is not a violent person, let alone a coldblooded murderer. I would not have employed someone like Linda if I felt they were capable of murdering someone.'
Carty and Jovelle are convinced that her work as an informant is somehow linked to the murder of Rodriguez, and may even have been an elaborate plot to set up Carty by criminals who discovered her role as an informant.
It was never suggested that Carty kidnapped or killed Joana herself. But according to the prosecution, the men who stormed Rodriguez's apartment in Houston at 1am on May 16, 2001, who beat and bound its two male occupants, stole cash, and abducted Joana and her child, were acting at Carty's behest.
There was no forensic evidence linking Carty to the killing of Rodriguez. Her conviction rested on the testimony of her alleged accomplices, who admitted planning and perpetrating the crime. None of these men faced the death penalty - only Carty did.
The prosecutor, Assistant District Attorney Craig Goodhart, described these men in his closing speech to Carty's trial jury as 'an armed robber, a dope dealer, a drive-by shooter and another armed robber'.
But this, he argued, only made their story more credible. 'Welcome to our nightmare. If you were going to kidnap someone and execute them, who would you go with?'
As for the car in which Joana's body was found, Carty says she had lent it to William Arvizu, a man she knew through her informant work.
But if he knew the truth about themurder, he took it to his grave - seven months before Carty's trial, intruders broke into his home and shot him dead, along with his wife and five-year-old daughter.
It was a professional, gangland hit: could he have been murdered to make sure he could not tell the truth about Rodriguez?
Carty's motive for murder seems equally questionable. Here the prosecution case rests on the testimony of Carty's former partner, Jose Corona. But Guerinot failed to inform him that under Texan law he did not have to testify at all and could have invoked the so-called 'spousal privilege'.
Corona later said he was certain that Carty was not capable of murder, and had he known about the privilege, he would have declined to give evidence.
Once convicted, Carty was moved from the county jail in Houston to death row in Gatesville, and the grim routine she has followed ever since. 'I get up at four in the morning - that's breakfast time, when the food cart gets here.
'I can't go back to bed because you can't sleep on a full stomach. Lunch comes at 10.45am. So I'm up in my cell until 11.30am, when I get ready for work.'
<As for the cell, it has a steel mesh door so 'you can see right into it, even when you're using the commode - a toilet and sink in one. The room isn't much longer than the bed, and it's not much wider, either. You can cross it in one step.
'There's no chair, just a small table, and everything's made of solid steel. My mattress is pretty thin, and it's torn, with stuff falling out of it. I've been requesting a new one for the past two years.'
There is just a small locker for her possessions. She gets one shower and a clean outfit - which could previously have been worn by anyone - from the prison laundry each day.
An avid reader, Carty says she likes romance novels, non-fiction and thrillers, especially the work of bestselling author Martina Cole, one of several celebrities now backing her case. Cole is planning to visit her this month.
Unlocked from her cell for four hours a day, Carty spends two at work - knitting and sewing. Then comes recreation. 'I have an option to watch TV for two hours or I go outside. I love jogging - I do laps around an area about half a football field.
'We're only allowed to mingle with three people at a time for security reasons. It's not always the same three: they mix us up every six months. We never mix with the general prison population.
'We're isolated. I don't have friends among other inmates because I choose not to. There's a lot of backstabbing.'
Among the 451 executions carried out in Texas since America restored the death penalty in 1976 - more than a third of the United States' total - three have been of women, including one since Carty's arrival.
On the night in September 2005 when Frances Newton was executed by lethal injection for murdering her husband, son and daughter nearly 18 years earlier, 'most of the guards were happy', says Carty.
'You have some who are sympathetic but they cannot afford to show it because they would be accused of fraternising with inmates. And then you have the plain old ugly ones, the hard ones, and they cheered. One officer told me Frances got what she deserved.
'But I was pretty devastated because I knew that, like me, she was stuck with court-appointed attorneys and she had no access to a good defence, even in her appeals.'
The day before my meeting with Carty, I visited the home of Jovelle, and watched her two sons, Jhouri, four, and Caden, two, riding happily around their garden in an electric toy Humvee.
Almost two years ago, Jovelle told me, the prison had abruptly announced that children could no longer visit Carty. 'That was a huge blow to her. They're the only grandkidsshe has, and she adores them.'
Jovelle, who like her mother has a degree from Houston and works as a pharmaceutical technician, adds: 'I'm sure she's learned to function, just as I have. She's very focused on her appeal. But it's like you build a mental wall, and at any moment it can crumble.
'I've been through the whole list of emotions: not eating, not wanting to talk or do anything. I saw a psychiatrist and she told me, "I don't even know how you manage to get up."'
When I tell Carty about seeing the boys, she breaks down. 'Oh my, you're going to make me cry. I've never held them. I've never touched them. I've only seen them through here,' she says, gesturing at the window that divides us.
'Now they can't come I miss their chubby cheeks. That's the hardest part about being here - not being around my family, not being with my mum. And it's hard when she and my daughter come here.
'You want to cry because you see the pain they're going through, but you try to control yourself. Jovelle will excuse herself and go to the bathroom and I know she goes there to cry - when she comes back, her eyes are red.
'It's hard being on death row. It's like looking at a movie or reading a book and discovering that you are the main character.
'And having people say you did something and you know you didn't do it - that's the hardest part of all.'
Carty's case was rejected last year by the Fifth Circuit court of appeals, one tier below the Supreme Court. Although the judges stated their decision had been 'close', they still concluded that Guerinot's deficiencies were not enough to reverse Carty's conviction or sentence because she had not managed to prove that a better lawyer would have produced a different outcome.
Now, under the vagaries of United States law, the Supreme Court petition filed by her current lawyers from Baker Botts, which is working closely with the UK human rights group Reprieve, has to rely mainly on a highly technical argument. It is that the Fifth Circuit's ruling conflicted with decisions reached in other parts of the United States.
However, in more than 95 per cent of capital cases, the Supreme Court declines to hear a final appeal at all, and simply issues a twoword refusal: 'Certiorari [detailed re-examination] denied.'
If the Supreme Court turns down Carty, the only man with the power to save her life will be Texas's Republican governor, Rick Perry. In the nine years since he took office, he has granted clemency just once, while more than 200 prisoners have been executed.
'There's a lot of things the British Government could still do,' Carty says. 'But when I lost the appeal in the Fifth Circuit, I got the same feeling I had when I was sentenced to death. It was like reliving that dreadful moment all over again.
'During my trial, I had to sit there and listen to people lie, but the jury bought it. My last prayer will be at least to let the truth come out, so my mum and my daughter will not have to suffer any shame.'
After an hour, our visit time is up. Linda stands to be led back to her cell, while I head back through a series of gates and the razor-wire fence to the world of freedom.
'I hope you can do me justice, because this is not a game,' she says as we part. 'Don't forget about me in England, OK?'