Plex requires an Internet connection to claim the server. The claiming process requires communication with hosts at plex.tv.
You might be able to run the server unclaimed, but anything that requires a Plex Pass will not work (the server is not registered at plex.tv, so Plex cannot verify the Plex Pass). Remote access won’t work either. Plex changed the claiming process several months ago. See New Claiming Requirement for Windows .
You can also run Plex without an Internet connection, but not without limitations. See [HowTo] Use Plex with No Internet.
Your best course of action is to re-address your network to use private addresses.
