The wire between the camera and the main unit carries the camera signal only. The power comes thru another power wire attached to the vehicle electric system. From what you said there are only these two connections to the main unit.
Since the unit powers up it has power.
Since the picture is the problem the problem most likely lies in the camera itself or camera wire.
So next I’d like you to remove the camera and bring it close to the main unit bypassing as much wire as possible. If the wire has connectors take it apart there. If not cut it and strip it marking the ends with tape which you number so you can reassemble afterwards.
Where do you live?