No one can tell you whether your case is viable or not without a lot more than just your version of the story; your lawyer would need to read the contract between you and the "warranty" company (it actually is a service contract, but I digress); you would have to have the car inspected by an independent expert, and your lawyer would have to see this report as well. Only after these materials are made available can one venture an opinion as to the viability of your claim. You should contact a qualified consumer lawyer (www.naca.net) and take it from there.
A contract would need to be provided for proper advice to be provided. Until then, no one can really tell you if you have a case or not. I reccomend speaking with local counsel in order to give them a chance to reveiw your situation in greater detail.
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Sounds like a "battle of the experts." This is not unusual in a lemon law case. Here, it's a bit more of a breach of contract case if they are not dealing with you in good faith. Regardless, you should have local counsel specializing in lemon law and auto fraud look at this. Find someone competent to review your issues here: http://www.naca.net