If so you may have left over registry entrys. You will need to uninstall the gog version if thats the case and then clean all traces of the game out of the registry and reinstall it.
However, simply reinstalling the game fixed the issue for me. The reinstall also worked in a matter of seconds. Apparently the installer noticed that the files were already there, and just fixed the registry, so that the game didn't ask for a serial any more. Smart. :)
If not start the game as admin and then it should stop asking for a serial number and start normal.