If you bought this used car with a warranty, then your warranty governs what rights you have. YOu need to review it yourself or hire a lawyer for help, since as is true of almost all contract questions, no one on Avvo can analyze the exact language in a contract they haven't seen, so you're going to need to review it yourself or hire a lawyer for help.
If on the other hand you bought this used car "as is," without a warranty, then pretty much all the rights you had, you had BEFORE you decided to buy this car - the right to test drive it, inspect it thoroughly inside and out, have your own mecahnic inspect it, the right to review its maintenance records and its CarFax reports, etc.
If you didn't do your "due diligence" to know what risks you were assuming, then you're left with whatever rights you got in the purchase contract you signed. Again, no one on Avvo can guess what your contract says, so you're going to need to review it yourself or hire a lawyer for help.
Disclaimer: I'm only licensed in CA. Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.