My laptop (a Clevo D900K) had a curious problem. It would show three blinking lights (num lock, caps lock, scroll lock) when powered on, but only for about ten seconds. Then the three lights stayed on, for another ten seconds, and then the laptop powered itself off.
The week before my vacation, I was unable to use the laptop. It would post and boot, upto the startup of gdm ... and then it powered off. This was annoying!
The shop (excellent service btw) didn't find a solution. Googling the problem was not easy.
The problem is now solved.
Tightening the screws of the video card solved the problem. Hope this helps other people with the same issue...