Hello,
Rather difficult, to say unlikely at least from a non-functional machine, it is supposed that the "product key" used to activate the product it was obtained somehow and stored somewhere. Perhaps by asking in more specific forums about Microsoft products you might find a better answer to your question, whether it is a physical or virtual machine your problem does not change.
If you had a working copy, not necessarily recent, of that same virtual machine, solving your "problem" could be much simpler. You can find several possible methods on the internet.
Regards,
Ferdinando
