Re: Odd problem
A: Bad GPU from overheating a really lot
B: full HDD
This happened with my HP NC6000 and it turned out that the HDD was pretty much full. Windows needs 500 MB in the HDD to run, make sure it hasn't filled up completely.
Though with the fact tht I'm probably the only person on earth who uses fricking 40 GB HDD's, I highly doubt that's the case. Good thing to check anyways.
Best way to check that since the computer won't stay turned on is with an ATA/API bridge. Plug in the drive and check it on a foreign computer.
Another thing that could also be wrong is the mother board. If so, it could be a capacitor, could be something is getting way too hot, anything really. I had that issue as well with the same laptop, same effects, but two symptoms.
In any case check that the HDD isn't ful first, and if not have an IT look at it. It is their job after all.