It seems that some time ago, Plex changed how to claim your server, and you cannot simply access the bundled web app and claim the server. You must follow the steps here:
Specifically, it points out you must right-click the plex icon and choose “Open Plex...” and it should prompt for claiming.
If that still does not work, then it’s likely your server is claimed under a different account… somehow. If you are the owner and manager of the server itself, then use the steps to reclaim your Windows server here:
It involves entering your Windows registry to edit or delete some entries. Our local forum ninja @OttoKerner has made an article on how to automate the process by creating a .reg file that will do exactly what needs to be done without the possibility of deleting the wrong registry entry:
Give each of these articles a try in order, and let me/us know if they helped.