When you uninstall, use the uninstaller that comes as part of the installer. Or use something like AppCleaner. And then still manually go to the Library folder to delete any stray folders and files. And reboot after uninstalling and installing.
WHat hava version is installed? If it's a version 8.x, that could be the problem (Yes, I read that they rolled back..)
The roll back process may not be perfect.
You may want to stop the server. Copy/ novel all of the databases to a convenient folder. The uninstall and reinstall/update FMS. Once newly installed you should have full functionality.
Your mileage may vary.
Had a similar issue with an portable development server. I bring it to my winter ski apartment. The issue is I can't reserve the IP address. So when I show up it usually gets a different address. When it does I have to uninstall / reinstall FMS to get it to work.
Sent from my mobile device... Please excuse typos.
Thanks to all for your responses. Unfortunately we may never know how to resolve this one as they have decided to stay with 13.3 on Mavericks for now since it is working for them (...kind of). Their "plan" is to wait for 14 and then upgrade to Yosemite and 14 at the same time. Not unreasonable I suppose, but I would have liked to take another shot at the reinstall again following an uninstall and manual cleanup of the FileMaker Server folders.