Do you think it would be fast enough to mine bitcoins or something like that or would the power bill exceed the profit?
Not even close. Mining on general purpose CPUs is like solving a Rubik's cube where you're only allowed to make one move/twist each year.... agonizingly slowwwwww.... You'd want to mine on dedicated GPUs. AMD/ATI cards seem to perform the best... For the system to be useful to anyone, you'll need more than 2GB RAM. Especially is you're running Windows or X (Gnome/KDE/etc) You're best bet is to donate to it to someone who doesn't know how lame the system is, or sell it for parts. You'll probably net much more selling it for parts. Then you can use the cash to buy the current high-end machine.
Yea I think that sounds like a good plan. I was looking into the bitcoin thing today and saw some dedicated machines for it that weren't too pricey and I thought it seemed like a good idea. Then I read a little more on mining them and saw that the "difficulty" is increasing by like 100%/month so it's going to start taking significantly longer. Not sure if it would be worth it or not then.