If you have no floppy drive then the only other option is to make a bootable CD (if you can ask someone else with a CD-writer to make the CD for you). This is only necessary if you want to install Win98 or WinMe.
If you install WinXP, you need to boot with the CD and the formating and basic partitioning functions are in the first few question in the installation process so at this point it's certain that the CD will be readable. As a side note, if you are able to boot from a CD, then any issue with your hard drive or the former operating system doesn't really affect this since it's the Bios that handle everything at that point.
As for the Cd key, if it's WinXP Professional, then pretty much any key can be used. They only check when upgrading with a service pack (but they allow nearly all known illegal key) and when you go on Windows Update (they are more restrcitive there but there is an easy way to get around their "security").
However, if it's a WinXP Home edition, then problems can arise since this version is far more restrictive. I can't tell more about it since I never really worked with this version.
@AngelofDeath5: Everyone are welcome to help around on such topic, it's not exactly an Admin-only problem