if you registered the game when you got it, can't blizzard help you with something here?
also, when I lost my sims cd key, I found a shareware program that retrieved it off of my pc. this requires that at one time you inputed the cd key, however. good luck. their web page describes manually searching your registry for the number.
sims serial number retrieval help...
http://www.simsplus.com/help/serial/serial.htm