Try this:
Do a scandisk on the whole drive (c: + d: + e:) with surface check, from ME first, then if nothing's found, try it after booting from the XP CD (it should be possible, if not, try from Me's CD). If you can't scandisk from the CDs, try a third party disc scanner.
The other thing you can try is to momentarily unplug the primary master drive, and plug the one you were given instead (temporarily taking the other one's place), then try to install XP on that drive. How small is your tower to not have room for a new disc? Because mine is only a medium tower, but I have 5 3"1/2 and 4 5"1/4 slots.