What is the name of your state (only U.S. law)? Ohio. I need to know if the Ohio lemon law applies to private sales as well as dealers, and what options do I have if the seller refuses to refund a reasonable amount of the money I paid.
Let me guess... You didn't take or make the time to have the vehicle inspected by your own mechanic before buying it, did you?
An informed purchase is a smart one. If you had had the vehicle inspected before purchase, then you would have known that it had problems, and its quite likely you would not have bought it (since you claim it to be a lemon).
Since it sounds like you did not have it inspected, and unless the vehicle came with an express warranty IN WRITING, then you bought it AS-IS, with all its problems (seen and unseen). The seller is under no obligation to return any money to you because of problems you should/could have found out about before buying it.
Congratulations on your purchase, and enjoy your new car!