You can locate a Parallels Desktop for Mac key used on your Mac using a Terminal command.
Note: The instructions below are only applicable to subscriptions.
Start the Terminal (Finder > Applications > Utilities) and execute the following command:
prlsrvctl info --license
The output will give you the serial line with numeric codes in the following format:
The more activation keys you used on the Mac, the more codes you will see in the Terminal.
Copy the contents of the serial line and send to Parallels Customer Support.
For other ways to retrieve an activation key for Parallels Desktop for Mac, see KB115424.