Is there any feasible way to match up a current install of Office 2004 to its physical install disc or serial, so you can tell which copy you used to install Office in the first place?

We've got one G4 with Office 2004 currently installed that needs Office removed and reinstalled (due to some glitchy Entourage settings). This is one of four systems in the office, each of which have individual copies/registrations of Office 2004 installed. Problem is, I don't want to willy-nilly reinstall one of the other three copies of Office in case the disc I pick is actually a copy still installed on one of the other systems, in which case one user or the other would be locked out of Office.

Does that makes sense? Basically I need to figure out which disc I used to install on that particular machine, but AFAIK there's no way to match the disc's serial to the install... Grrrr!