I suppose that depends on your purchase contract and your warranty. Most likely, the answer would be no. A used car is generally sold "as is" and the dealership bears no responsibility for what happens once you drive off the lot.

lol... No, you can't get a refund on a car that's 6 years old with 54,000miles on it and with engine damage. a) Most dealers don't even give you a refund within 5 minutes of buying the car, so 6 years is a big stretch. b) It's been more than half a decade - even consumer goods like TVs, etc. only have a 30-day return policy or maybe a 3 year extended warranty. c) You would have to prove that the dealer took your specific car, dismantled the engine, put a small enough dent in the valve so that it bends after 54,000 miles (but runs perfectly before that), then re-assembled the engine and sold it to you. Good luck... d) The dealer is merely a middle man. They didn't make the car. If you were to sue anyone it would be the manufacturer, but you would lose that case at the outset. e) No manufacturer can be sure that every vehicle they make will work problem-free for a decade. Problems arise, and that's why there are people called mechanics. You might want to call one of them. f) Timing belts will break if not properly taken care of and/or not replaced at the specified interval. Check your owner's manual for the recommended replacement time of your timing belt. (By the way you probably have a serpentine belt not a timing belt) g) The company that made your engine, and in turn the company that made the valve, has made thousands and probably millions of valves in it's time. Manufacturing defects, installation mistakes, metal decay, etc. could all be reasons for your bent valve. h) I don't know what a 'car note' is, but if it's anything like a bank loan that's irrelevant. Someone has already bought the car for you and you are merely paying them back. Whether you bought the car outright or financed means nothing. i) An extended warranty would've covered this damage, but you obviously didn't opt for one. It may or may not have been offered by the manufacturer but you could've bought one from a 3rd party. j) I'm out of things to say. You don't have a case. Get over it. Cars aren't perfect. Move on. Fix it or sell it. Bye

Despite the vehicle haveing low miles, there is usually a milage limit AND a time limit for timing belt replacement. The car is 7 years old. In the end proper upkeep is up to you the owner. I hate it when customers try and blame dealers/mechanics for problems that are the CUSTOMERS fault. You don't want to part with your money to maintain your vehicle when you are suppose to...you are sure going to part with more of it now. So, now be a man. You can only blame yourself for this one...