You are not necessarily at fault, but you still owe it. If you don't pay it, then you will probably spend more than that fighting over it. The law generally follows morality. That means if you make a deal, such as by signing a contract, than you will have to live up to it one way or another. Thanks for asking and good luck.
This answer is for general purposes only and does not establish an attorney-client relationship. The law in your state may differ and your best answer will always come from a local attorney that you meet with privately. If you need a Consumer Law attorney, click the link above to find a Consumer Law attorney near you.