Hello Ben,
Welcome at the VMware communities.
If it is the guest OS disk drive serial number that they are checking then you can use the old serial.
If they check the host OS disk drive serial number then you are out of luck.
For guest OS.. when you loaded up the backup for the first time in VMware Workstation, it probably asked a question "did you copy or move the VM?".
The correct answer was "move", in the other case hardware UUID's are regenerated and that would explain the licensing issue.
--
Wil