Your intent isn’t technically relevant to copyright infringement. It tangentially factors into a Fair Use defense, but it’s really beside much of the point. Your valid license is pretty important, though.
Take a look at the six exclusive rights a copyright holder (Microsoft, in this case) owns. Microsoft is the only person allowed to make copies of Windows XP Home available to other people. If you’re only downloading, you’re not infringing on any of Microsoft’s rights, because you paid them for a license to make a copy of Windows XP on your computer. Of course, BitTorrent simultaneously downloads and uploads files: in no case do you have the right to make copies for other people. That’s instant copyright infringement, no matter what.
Let’s assume, then, that you’re on Usenet or FTP or whatever. In this case, the license gives you some privileges. They’re probably limited to installation of the OS, not downloading and replicating the install CD so you can replace your lost one. Do note that violating the terms of the license would make your downloading an infringement of Microsoft’s copyrights, because you’re probably only licensed to go from CD to Hard Drive and that’s it. Microsoft’s (like everyone’s) EULA’s are very limited.
However, some good news: assuming you’re being honest, and you’re not running a WinXP bootlegging operation out of your dorm room, you’d probably be able to defend yourself against an otherwise successful claim of Copyright Infringement with the Fair Use defense. Stanford has a lovely website explaining how that all works.
Of course, this is all moot, because Microsoft probably isn’t going to sue you for downloading XP. Their lawyers are on the lookout for Windows 7 pirates this week — you picked a good time to lose your XP disc!
I am not a lawyer, and this is not legal advice. I did rather well in my law school Intellectual Property class, but you should call up a real lawyer to ask about this for legal advice.