What would you want to do with that product key once you found it? Or, put otherwise, how do you suppose it to work?
What we usually advice:
1. Boot from a Ubuntu Live disc (free download) and copy all those files you forgot to backup to an external disk, and then to your own PC.
2. Do the prescribed system recovery to go back to factory conditions. This won't need the product key.
Kees
Preinstalled Windows Vista Home Basic on kids laptop has stopped working and no product key to be found anywhere on laptop or original packaging/documents. Can I get one/buy one that will work without having to reinstall windows and lose all their (un-backed up!) files?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic