Almost all private sales between individuals are on the "as is" basis, so goes the phrase "buyer beware." Unless you had made some time of warranty or guarantee arrangement during the sale and have it in writing and signed, you often have no claim against the seller. It is generally the prospective buyer's responsibility to inspect the vehicle for himself or have the vehicle inspected by an auto professional (dealer or independent repair facility) prior to purchasing a vehicle.
Now, "as is" laws don't provide protection for those who are guilty of fraud. If the seller makes a false statement about the vehicle and the buyer can prove it, there is grounds for legal action and, depending on the state, that seller can be held liable for not disclosing a material fact of the transaction to the buyer by remaining silent.
If you paid a significant sum for the vehicle, you would be best to seek advice from an attorney.