As far as I know, product keys are not stored on the CD. You'll most likely have to purchase another copy, of if you still have Windows XP installed with the key you used, there are some programs that will extract and show your product key, but I've never actually tried it myself.
as far as I know it is not installed on any computer.
That's bad news. The key is the key, so to speak. Those keys cost money.
Considering the end-of-life or whatever they call it for XP, perhaps now is a good time to step up to something newer that will be supported for a decade, like Windows 7.