For a rock-bottom machine, here's what I'd search for at newegg.
Get the cheapest socket AM2 athlon 64. Avoid sempron.
Get an MSI or ASUS AM2 motherboard with integrated everything except for video. There are some mini-ATX mobos for around $90 that are really nice.
Get an Nvidia 7xxx series video card, the most expensive you can fit in your budget. I'd suggest 7600 series at least, or the money is IMHO wasted.
Get 1 or 2 gig of DDR2 memory, as your budget allows. Quality name brand is more important than top memory speed but you probably won't go wrong buying DDR2-800 speed.
You'll probably need a new power supply, but your old case should work if it fit an ATX motherboard.
That's about all you need. Cannibalize your modem and hard drive from your old computer if they still work and the HD is big enough.
Realize you can do the exact same thing with Intel cpus, but I'm not so sure how much performance you get at the cheap end of the newer intel conroe cpus. I'm much more familiar with the price/performance of the AMD cpus, and I know that the low-end AMD cpus are a bargain. You get a heck of a lot of performance for the price.
For another slightly cheaper but more dead-end alternative, pick up one of the socket 939 cpus, motherboards, and use DDR memory. Yea they're at the end of their technology lifecycle, but that also means that you get good performance at the bottom of the price scale.
