The dealer is entitled to enforce the original contract on its terms (which would mean no refund at all). A purchaser can rescind/cancel a contract, if the purchaser can show that the purchase was based upon a material mistake of fact concerning the subject matter of the contract (i.e., the vehicle). However, to actually recover the deposit, the purchaser would have to sue in court, because the dealer won't voluntarily accept the rescission, without some sort of consideration (which, in your case, is the $2,000).
The same rules as above exist where the dealer committed material misrepresentation of the vehicle's condition, age, value, etc.
Your recourse at this point is to take the $2,000 and sue for the remainder. But, if the dealer provides you with a check displaying the terms, "paid in full," or "full satisfaction check," or similar, then you can't cash the check, or you will have agreed to the refund as full payment for your contract release.
Also, if you are required to sign a release agreement, then this, too, would terminate your right to sue.
Bot***** *****ne, there is a way to beat the dealer, but it's not a slam dunk. You must be prepared to fight for your rights.
I realize that my answer may not be exactly what you were hoping to read. However, under the circumstances, the best that I can do is to explain what the law is and is not, so that you can avoid expending valuable resources looking for answers that do not exist, and concentrate on the options that are actually available.
I hope I've answered your question. Please let me know if you require further clarification. And, please provide a positive feedback rating for my answer -- otherwise, I receive nothing for my efforts in your behalf.
Thanks again for using Justanswer!