Verify that Plex server is still running on the old machine. Start it, then watch the Plex task tray icon. If it vanishes when you mouse over it, the server is crashing.
If the icon stays, you can try to re-claim the old Plex server into your account. You need to reclaim your server, but don't dare to touch the Windows Registry
(you better shut down the new machine while trying this)
