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Hmm, well, if you do have the game installed (although, it sort of sounds like you don't), there is software that retrieves product keys from the system. I can't remember the name of the one I used but there are lots - you can try googling for "key finder"/"key restoration" or something similar and you're bound to find something.
However, if you don't have it installed now, nor have you had it installed before on this machine, then I don't know. You could try ringing customer support but with a game this old, I sort of don't expect results.
We do what we must / because we can. / For the good of all of us. / Except the ones who are dead.