I took it to a shop, and they said they'd keep it in observation to figure out what was wrong with it. After a whole day of it never shutting off, they determined it had probably been dust creating short-circuits.
Now, I use F-Secure antivirus, but apparently the guy at the shop missed this, because he says he thought the computer didn't have an antivirus installed, and tried to install Norton Antivirus. He said that during said install, the computer rebooted, so he thinks it was a virus that was making the computer shut down in the first place.
He said he will run some tests (including installing a hard disk they use for this kind of things) and figure out if he can isolate the virus or if he'll have to format my HD.
Is it possible for a virus to create the problem I described?
If it has anything to do with it, I have Windows XP Pro, on an AMD Athlon 2800+, 512Mb. I use a Zone Alarm firewall and F-Secure as an antivirus.