I had this same problem. It has to do with your font management software. If you're like me and are using Universal Type Client for font management, go to your system preferences, select "Universal Type Core," System Preferences will prompt you to close, then reopen, and you'll see a check box that says "Start Universal Type Core at Login." Make sure it's selected, then restart InDesign. Should work like a charm. That invisible little font app needs to be running in the background for InDesign to access fonts properly. When it's not running, InDesign freaks out. Any little update you, or your IT folks, run to your font software could possibly turn that check box off by default.
