I have an interesting dead laptop. This Gateway MX-6931 overheated on a bed, did not shut off (possibly because the CPU wasn't doing much, so the motherboard was hotter), and now refuses to boot.

The interesting part about it is, unlike other dead laptops, this one will POST and find the drives. It will spin up each drive (one hard drive and one DVD burner). But, after the POST when it comes time to actually boot one of them, the laptop refuses; it simply blacks the screen, and does nothing. This is regardless of which device is set to boot, or how I override it in the boot menu.

Any thoughts as to which component is failing to do the job for which it is responsible?? I'm quite at a loss as to what I can do with this machine. :(

Seems to me like the VGA chip isn't working well. (Read: motherboard).

That is most likely the very source of heat you felt... and first to go from overheating.

I too suspect that the VGA is faulty. Better you take it to a good service person.