Changing your Plex account password unclaims your server (removes it from your account).
You need to re-claim the server.
On Windows, the information is stored in the registry.
See these two documents:
After editing the registry, reboot the PC, launch Plex, and try to claim it.
Also, make sure the browser has access to the local network. See Important note about the Plex Web app - Local Network Access .
Where Plex stores server settings, claiming information, etc. varies by platform. Details in the “Why am I locked out…” document.
Windows: Windows registry.
Linux: preferences.xml
Mac: plist file