It's possible to recover the Windows XP license key from a running copy of Windows if you've lost the install key -- a tool called ProduKey can do that for you. But if you have neither the PC nor the license key itself, then sadly nothing can be done.
This is why Microsoft has a large warning notice on the license key, and why they urge you to keep it in a safe place.
Note: If your old copy of Windows XP came with the PC as a preload, it can only be used with that PC anyway. It can't be transferred to another computer. (Copies of Windows bought with a PC are licensed for that PC only.)
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