It sounds like a bad connection sure enough. And when you talking about a bad connection it could be alot of things to check out. Switch,fuse box, bad ground, etc..
I used to know a fellow years ago who owned a 92ish Dodge truck that it would crank right up when cold, but would not start up until it got cold again. Another words he could not shut it off if he went inside some where and had to wait until he got home to shut it off. He took it to the Dodge place and they could not fix it! They gave up and said "Sorry we don't know what causing it!" The trucks warranty was up on that particular system of the truck. I don't know if he ever got it fixed or not.
Have you tried resetting the computer?
