If you go into device manager, is anything in an error state, or detected as an unknown device?
The battery doesn't work in the laptop? Do you need the battery in for the AC to work properly? If not, try it without the battery in.
Try cleaning out the dust by blowing some canned air through the vents.
I don't think it would be the hard drive because the system wouldn't just cut off like that, it would probably just lock up, but remain on.
I'm not very good with laptops, but If none of the above works, I think there may be something wrong with the internal power connections, or the motherboard is going.
EDIT: I just had an idea. how about you let it sit in the BIOS for a few hours, and see if it cuts off. If it cuts off here, then it's probably a hardware related issue. If not, then it's something else
Edited by Sterling14, 25 March 2009 - 07:00 PM.
"I think there is a world market for maybe five computers." - Thomas Watson, Chairman of IBM, 1943