Uuuugh! This computer is driving me nuts and I can't quite decide whether to toss it in a dumpster, to repair it myself, or to send it out.

THE COMPUTER: Compaq Presario V2000 laptop.
THE PROBLEM: After several minutes of operation, it makes a popping sound from the speaker and has total power failure. The power light is off. Push the button and no response. After a few minutes, with the battery out and the cord removed and then replaced, it will restart, sometimes.
ELIMINATED?:
Power Brick: I have swapped out power bricks and checked the output
with a meter.

Battery: The battery was replaced three months ago and seems fine. The
problem occurs when the computer is operated with the battery removed.

Fan: The fan operates intermittently (apparently as designed) when the
computer warms up. When it operates, the evacuated air is warm but not
hot.

What to do? My thought is the problem is that the system is detecting it is overheated or there is a problem with the power supply somewhere. Is this something that is goint to require a motherboard replacement? I don't want to send the computer out because it has my work files on it which contain sensitive information. Suggestions?

Thanks!