@Will > The database is not linked to the license key; there could be two separate installations with different libraries on the same key. I'd suggest you file an inquiry ticket here and provide our support team with your license key and email address for your rekordbox account - they can deactivate the old computer so you have both licenses available again.
You could recover the data from the old drive, but would need to make a few edits to the settings files and relocate tracks in order for them to play.
Are you on a Mac or PC?