When you launch Filemaker on the new machine, and choose File -> Open Remote, what servers (listed in the left pane, under Local Hosts) do you see? Is the list (which may be a list of 1) the same as the list you get when you do that on any of the other machines?
Are you running FMPro on windows in a domain? If you are, this is a known issue, that occurs because your system-time and the active directory time are differing more than five minutes. If that happens for some odd reason FM installs a corrupt version of the file "server.pem"
The file can be found in the same folder as the application. If the file is about 4kb it is corrupt, it should be about 6kb. Simply copy it from a computer that does not have the problem (even a computer with fm10 or fm9 ;-))