If we bought a car from a used car dealer and less than 24 hours later we found a fire hazzard with the wiring, can we take the car back and get a refund?

Like many states, llinois's Lemon Law does not cover used vehicles. But maybe to your advantage here Illinois law has specific language that a dealer must use to disclaim an implied warranty. If the dealer doesn't disclaim an implied warranty and you buy a used car that is less than four years old, you have a power train warranty (engine block, engine head, internal engine parts, oil pan, gaskets, water pump, intake manifold, transmission, torque converter drive shaft, U-joints, and rear axle). The warranty lasts for 30 days, and says that, if the car is less than two years old, he must pay 50% of repair costs; if the car is between two and three years old, he must pay 25% of repair costs; if the car is between three and four years old, he must pay 10% of repair cost.  The other laws that can help here are issued by the Federal Trade Commission (FTC).  It has what's called the Used Car Rule that requires dealers to provide consumers with a Buyer's Guide with warranty and other types of information. If the dealer has in any way failed to abide by the FTC Used Car Rule, you may have the basis for a legal claim. Then there is your state Unfair and Deceptive Acts and Practices (UDAP) laws. If the dealer has, for example, made verbal promises or didn't tell you about issues relating to your used car, you may have a cause of action. There is also your state UCC (Uniform Commercial Code) and the Federal Truth in Lending act.  If there was fraud or misrepresentation then there is contractual relief.  Good luck.