ThinkPad screen keeps going out

It appears there’s a short inside my T41p. The screen will be fine and then it goes gray, then goes out. If I try to reboot it often doesn’t help. If I push firmly around the keyboard and try to reboot it seems like this does the trick. But then if I move the screen or push too hard the screen goes out again.

Firing it up with a boot CD doesn’t help. And, as I said, when the screen is working it’s working fine and looks good and everything operates normally.