At some point after upgrading FileMaker Server 14v3 (also referred to as FMS 14.0.3, specifically 18.104.22.1682) to FileMaker Server 14v4 (also referred to as FMS 14.0.4, specifically 22.214.171.1242) using the updater file fms_updater_126.96.36.1992.dmg that was released on November 12 access to the web console was broken from remote machines, as shown in the image above.
After some experimentation and a call to FileMaker Support it turns out this is a known issue that arises from the updater. The only solution (as of November 23) is (cleanly) deleting the updated FileMaker Server installation and reinstalling using the FMS 14v4 installer.
There are a couple of things to keep in mind when doing this...
It's important that it be deleted using the official FileMaker uninstaller, but that can be a little tricky.
FileMaker support says that there should be an uninstaller application include with the new FMS 14v4 installer that you are going to run, but that is not accurate. The installer includes a tool for uninstalling FileMaker Server 13, and it only appears to be able to delete installs of FMS 13. It does not seem to "find" installs of 14.
There is however an uninstaller that you can use, one that was included with the original 14 install. If you go to ...
Library > Application Support > FileMaker
... you will see an application called FMS 14 Uninstaller.
That will do the uninstall that you need but before you run it there is one thing you really need to do:
If you have created any schedules or groups you will want to save them before deleting FileMaker Server 14 (so that you can then load them into the new FMS 14 install when complete).
This is, unfortunately, made somewhat more difficult by the fact that you can't access the server admin console where you can access the save function.
You should still be able to access the server console from a broswer on the server using:
Remote access using https://[host]:16000/admin-console won't work (this is why you are un/reinstalling) but http://localhost:16001 should still be fine.
From there log in to the FileMaker Server admin console. Then, from the top right, click on "Server" and select "Save Schedules and Groups...".
You should then see something happen. The file (called fms14_settings.settings) should be saved in your downloads file. If you don't see some kind of download animation (that will depend on your browser) it probably didn't work. And if you can't find the fms14_settings.settings now you will be out of luck later.
One common issue involves security settings. For this to work you have to disable (even temporarily) pop-up blocking in your browser. If popup blocking is enabled you will not be able to save the settings file, and you won't be warned of that.
FileMaker Server allows you to specify an additional database folder and the default backups folder (Database Server > Folders). This will be lost when you do the uninstall (not the folders or data in them, just the link to them) will be lost when you do the uninstall. You should make a note of any alternate database/backup folders before doing the uninstall.
You will then need to re-enter those folders into the new server installation prior to loading the saved schedule.