What rights do I have after buying a car from a used car company if I have problems

It would depend on your location (in some areas the law is more sensitive to consumer issues than others), whether the dealer made any statements as to the condition of the vehicle and what is written on the contract of sale. In most locations, knowingly selling a car with a major defect without disclosing it would be considered fraud but if the contract says that the terms of sale are "As-Is," that's saying you are accepting responsibility for the condition of the vehicle.