Forgot to mention that the key generator itself must be 'registered' to run. And of course, there's no-one left any more to create the key for the key generator!
Unless the software validates itself over the net or, (as f0dder said), is tied to machine identifiers I would have thought you'd be able to pull the registration info from wherever it's hiding, eg. registry, file, (AD is also a possibility), etc.
However, the very first thing you should be doing is creating a raw
drive image of the machine for backup. I say raw because you don't know what kind of registration magic is used and it's better to be safe.
Is that the one by TSM Inc and does no one keep registration info/emails where you work?