SLAMPP is a ready-built and ready-configured completely free bootable webserver on a CD.
1. Download it from here http://slampp.abangadek.com/info/
2. Burn it to CD
3. Boot your old desktop with the CD
4. Play about, learn. Decide if you like it.
5. Install from CD onto your old desktop
6. Insert your website code into /var/www/htdocs
7. Open a path through your router to the old desktop
8. Buy/scrounge a dynamic DNS service (for instance from no-ip.com, and there's others)
9. Install the little updater client program that keeps your dynamic address correct
10. PROFIT???
11. Follow the instructions at http://slampp.abangadek.com/info/ on how to make it more secure (change the root password for instance)