Look around on Craigslist in the free section. I've seen towers as new as Northwood P4s before near me (Philadelphia). Also, it wouldn't be too expensive to build a new super-budget pc.
(Can't post links yet but these are from Newegg)
ECS945TGCT-M/1333 - $43 - $10 MIR + $9 Shipping
Intel Celeron 430 (1.8Ghz, comparable to a late P4 but cooler and less power hungry) - $40
2GB (2x1GB) DDR2 OCZ Value Select RAM - $36.99 + $7 shipping
~$126
Reuse your Hard drive, case and monito, hopefully your OS. Add a video card of your choice (or wait a bit and do so, you could probably game a little better on the onboard GMA 950 than any onboard graphics from the early P3 era). You could splurge a bit for one or more of the parts as money allows. You could move to a dual core Celeron for about $20 more, or go better. A better motherboard and RAM would allow for more overclocking, which is basically more performance for nothing but a bit of time invested in tweaking things.
But that configuration as-is is nothing to sneeze at for as little money as it would cost. And if $126 dollars is a dealbreaker to move from a near decade-old computer to something more modern, you have more pressing issues to deal with than getting a graphics card.