2002 Ford Windstar Auto will not start after short drive (5

After driving about 5-10 miles and then stopping and shutting off the engine, I have to wait for the car to cool down before it will start again. Jump starting does not work either. Thinking that it may be the starter, I replaced it with a new one. The problem is still present. All fluids are at the proper levels. I've owned this vehicle for four years and this problem seemed to have started with-in the last year. When I turn the key, there is no "clicking" or any discernible sounds. All the lights work fine; The initial dashboard lights come on as normal; The radio, windows and other electrical systems work. As a Government retiree, I can not afford a full electrical dealership diagnoses at this time.