Re: garage ceiling fan
The safe way for you to check as a homeowner, with the power off, is to get a continuity tester. Test between the white wire and the ground wire. If you have continuity, then that is your "neutral" conductor, and the white from your light fixture needs that wire to operate properly. That might be a start. Two of the black wires are switch legs, at least that is how it sounds. But I can't say to do anything with those wires because I cannot see them, and could be dangerous, or you might fix your lighting issue, then half of your garage will not work.