You posted this under Lemon Law, which does not apply to used car sales between private parties.
You're fighting an uphill battle. When private parties sell a used car, the sale is ALWAYS as-is, unless there is some specific agreement to the contrary.
If you can show the seller deliberately defrauded you -- such as claiming it was just checked out by a mechanic or that the engine was just rebuilt, when those things weren't true -- you may have a civil case for fraud, but you aren't going to just get a refund. You will have to sue him, and that can take a while.
When buying a used car, it's always worth the money to get it checked out by a mechanic of your choice. Even then, there may be problems that go undetected unless it's too late.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
With no written contract, the question is whether or not there was an oral agreement that anything about the car's condition was being guaranteed. Buying a car in a private sale can be risky business because the law is very different from a car dealer sale. In a sale between two individuals, neither of whom is a car dealer, in most states the only obligation on the seller is to answer your questions honestly and not hide anything that they realize you would want to know about. If the seller lies to you or hides anything, that can be fraud in most states. They have to tell the truth about the mileage on the car too by filling out correctly and honestly an odometer statement for the buyer. And in those states that require mandatory emissions tests in order to get a vehicle licensed, many of those states say that if the emission/pollution equipment was disabled or removed then the buyer may have the right to cancel the sale. If none of that applies to your deal, then you may be stuck. To find out for sure, you need to talk to a local Consumer Law attorney. Call your local attorney's Bar Association and ask for a referral to a Consumer Law attorney near you or you can go to this web site page for a Free Online 50 State National List of Consumer Law Lawyers (http://www.ohiolemonlaw.com/ocll-site/ocll-locate_local.shtml) and find one near you (lawyers don’t pay to get listed here and most of them are members of the only national association for Consumer Law lawyers, NACA.net). But act quickly because for every legal right you have, there is only a limited amount of time to actually file a lawsuit in court or your rights expire (it's called the statute of limitations), so don't waste your time getting to a Consumer Law attorney and finding out what your rights are. If this answer was helpful, please check the box below.