I had something like this happen a long time ago in my old Tempo. If there's a short to any of the speaker connections, the head unit will automatically stop putting out any sound to all of the speakers. With my situation, one of the speaker terminals was touching some sheet metal from the door (both positive and negative touched) so it disabled output from the headunit.
I would pull the head unit out but leave it connected. Maybe try to hook up one channel of speakers at a time and see which one is causing the problem. It may work just by pulling it out of the dash and trying it. But, it sounds to me like there's a short to one of your speaker connections.
2013 Race Red GT/CS 6MT; Elec Pkg; RAAMat on the doors; Morel Tempo 5x7 coaxials; GT500 axle-backs painted black