Computer shuts down :(

I've had a seemingly curious problem for the past few weeks now. My computer (AMD Athlon 4000+ (2.41 GHz), 2GB RAM) shuts down randomly without a warning, freeze blue screen, or any other type of message. It just blacks out. The first time it happened was when I was about to play an online computer game (a rather old one, from 1999), at the exact moment I pressed Enter in order to connect to the server I had selected, though it had worked flawlessly several times before. Since then, the error has occurred:

*Randomly during fresh, cold boot ups.
*When I've been away for a few hours (usually I leave it on nighttime to download stuff), it's usually shut off.
*Randomly after extensive use (such as after a few hours of gaming, though this doesn't seem to happen very often).
*Somehow in relation to foobar (my music playback software) or the Mozilla Firefox browser, when skipping tracks or clicking hyperlinks, for instance (so, not totally randomly). A few times I even heard a subtle screeching noise from the HDD (I think) while clicking certain links, the last one I pressed shut me down. I've stopped using foobar now and that seems to prevent it from crashing as often.

I've checked the CPU temperature with a monitoring software and it seems to be OK (around 36C).

Also, after it shuts down, the busy lamp keeps blinking. I have to unplug the power cord and leave it for a minute or so until it stops and I can power it back on.

Any ideas?

Thanks in advance