Did you try running with just one memory chip or the other?
There are also some decent boot-from-disk memory testers out there that aren't to hard to find.

It definitely sounds like a memory flaw or a hardrive failure in a system file to me.

Problem: I can't generate bootable media off this computer. It doesn't have a floppy drive or a CD burner.

I haven't gotten around to taking out just one stick because all the stuff I would want to do would require more than one stick can provide anyway, so it doesn't actually matter. Since I'm piss-poor and will never be able to afford new memory again as long as I live, it ultimately works out the same whether I keep the stick in and can't use it or take the stick out and can't use programs.

Still, it's very odd, to me, that the problem only occurs when the computer is actually working hard. Wouldn't a bad piece of memory be just as likely to be accessed during a routine task as during an intensive one?

Check Newegg.com for memory. Really good prices there.

Still really too damn expensive for me right now, is the problem. I really have little money.

Any idea what kind of memory you use? I have some sitting around that I'm not using that you could have if it's compatible. I'll check what kind I've got when I get home.

Ah, types of memory: one place where my memory fails. I honestly don't remember all the options...