Odyssey Intermitent Starting Problems

10/01 Odyssey takes spells of not wanting to crank. It's not a starter as it was replaced deveral weeks ago for an unrelated problem. When this happens all door ajar lights come on as well as every other light on the dash. The electric windows will roll up and down with the ignition off and the key out. The starter make no noise or clicks like a solenoid trying to engage. So far, within between 2 to 15 minutes everything goes back normal and the starter cranks the engine. Any clues?

Actually after observing what goes on when it cranks right; all of the dash lights come on when the switch is turned on. They go out as it cranks. But the windows aren't supposed to go up and down with the key out and the switch is off. They do when it won't crank. They don't when it does. I hate electric gizzmo's on my cars.