Open ground on all outlets, voltage meter beeping on metal boxes and MC cable
Well, don't trust the no-contact tester to tell you anything but the presence of voltage somewhere close to the end of it. Beyond that they aren't much use.

From what you said in #4 you have an open ground. Also, if you used a 3 light tester and it told you you have an open ground, I would believe that.

Check your equipment ground connections for a bad splice and terminations for a loose connection. Also, if this is a garage with a sub-panel it is possible they miswired it and your ground back to the main is open somewhere.

Good luck and stay safe by working with the circuits off!