1999 Chevy Silverado starting problems

My 1999 chevy silverado 1/2 ton, 4x4, w/5.3 engine, auto trans, w/100,000+ mi. Has a starting problem. When I drive it more than 20 miles then shut it off, it will not start till the engine cools, about an hour. I had the starter rebuilt & a new silanoide put on, & that didn't work. I took the ignition & starter module out and put them in frount of the home a.C. No help. I put a new battery in and yes the alternater is charging, still no help. When it will not start, it do'es nothing, no clicking the starter do'es not try to engage or anthing. All other componits work fine. Any help? I forgot to mention that I tryed to start it in neutral & tryed holding the key in the start pos. & Shifting to neutral and no help. I put a new trans. In over a year ago but this just started a few mounths ago. Any help is greatly aprisheated, THANKS, & sorry for the bad spelling.