Fan works for heat but not central air?

Does the central air come on? Does the fan run if you switch it from Auto to On? If the answer to both of these questions is yes the stat is probably bad. If yes to the first and no to the second question, it is either the cooling fan relay or a broken fan signal wire from the stat ( the G wire). To prove this, turn the air handler unit power off. Locate the low voltage terminal board inside it(where the stat wires are connected) and put a jumper between terminals R and G, replace all the unit covers and turn the power back on. If the fan starts the problem is the G wire, if not its the relay. Verify this by doing the same test at the stat (R to G), the fan should not start. If it does the stat is bad.