Based on what you write, they appear to be in breach of contract (a warranty is a contract). Therefore, you could sue them for breach of contract for the money they should have paid. To win, you would need to show in court, by a "preponderance of the evidence" (that it is more likely than not) that under the terms of the warranty and the facts that they should have paid. Representing yourself "pro se" to save on legal fees may be a good option in a case like this, where the terms of the warranty (which you can present in clurt) will establish a lot of your case for you. You should be able to get instructions on filing a suit from your court.