If a signature was missed on my new car contract, is it still binding?

Yes, it could still be binding. A signature is not, in and of itself, "magic"--that is, it's not that the signature creates a contract. Rather, a contract is created when there is an offer (for example, buy a car for $XX,XXX.XX) which is accepted by the other party (for example, "I'll take it.") and consideration, which is either things or promises of value, are exchanged (for example, if you pay the $XX,XXX.XX, you get the car). A signature provides evidence that the parties agreed to the transaction, but as long as offer, acceptance, and consideration can be shown other ways--such as by testimony; by showing all the paperwork that's been completed, that no one would do unless they were buying a car; by putting down a deposit; etc.--the contract is enforceable.