Actually depending on your exact situation, it might be possible. If that computer you have originally came with WinXP Home SP2 already installed, then you can use this disk to reinstall it, and use the OEM CD key that should be on the sticker on the side of the computer (or in a drawer somewhere with the other documentation). Then you use the CD Key that comes with this disk to install it on your new machine. In this case, both copies are legal installations, you just used one disk which there's nothing wrong with. The CD doesn't care what key is used.
If the original computer didn't come with SP2 OEM version already installed, maybe it only had SP1, then I don't think that it will work. If of course you have the license key for it, then you can try to get hold of an SP1 install disk and install it, again that's completely legal, it doesn't have to be your original disk if you're using your legitimate license key.
TG2 pretty much said the same thing, I elaborated.