For that I'd go for something old. First see if it's actually fixable/usable, maybe you didn't try something back then that you could now.
Then go to ebay, and by category computers then components then CPU and mobo combo, then AMD. (even old intel stuff that's the same speed is way more expensive.)
You should be able to get a athlon XP or early athlon 64 that will cost you maybe
$30-55 for the CPU and mobo, they should use the same RAM as that old computer so you should be set.
If you don't want it to handle printing, I recommend FreeNAS. It will be set up and running in 10-20 minutes and you can start loading it up. It can even have streaming to say an xbox 360 set up. Really FreeNAS just wants about 512 MB of RAM, it cares not about CPU speed, so whatever you find should be able to do it amply.
Before I got my 3200+ CPU and mobo bought back from a friend after he upgraded again, my own server was running on a pentium 3. So it really shouldn't be difficult.