You could get a used computer for about $100 - 200 not including monitor if you check pricewatch.
Keep in mind that to run say KDE or Gnome you need 32 Meg of ram. 16 might not cut it. Also, many Linux distributions today are optimized for a Pentium CPU and will not run on a 486. Also, get a computer with CD-ROM. Maybe I'm just not too swift, but Linux is real hard to install via network or ftp site.
Here is one I found on pricewatch, but many places sell used computers. Compgeeks also has used computers or parts to build your own.