Thank you for your post.
If all other clients connect to a remote database, then perhaps the server.pem file is corrupt. Go to one of the other Macs that is working, and right-click on the application FileMaker Pro 10.0v3. Select the option "Show Package Contents". Open Contents -> Mac OS, and copy the server.pem to the non-working machine. Right-click the application FileMaker Pro 10.0v3 on the machine having trouble, and replace the server.pem file with the server.pem from the other machine. Launch FileMaker Pro 10.0v3, select Open Remote from the File menu, and you should be able to see the remote files.
Let me know if you continue to have difficulty.