I don't think it is bad power transitors. If it were bad power transistors, it would always move at maximum speed in the same direction when the EStop is released, whether the ribbon cable is plugged in or not. I am not familiar with the Supermax stuff so I don't know exactly what is routed over the ribbon cables.
My suspicion is that you have an encoder failure, either wiring or maybe the encoder itself. The reason I think this, is that when you plugged the Z axis ribbon cable into the y axis, everything sat stationary until you jogged the Y axis. With no feedback a servo will sit stationary until something generates a difference signal (jogging the axis) and then it took off. With no feedback, the servo never knows that the mechanical system has moved past the requested new position. Why you don't get similar behavior with the Y axis hookup, I am not sure. It may have to do with what is route encoder, it would be a good idea.
Are the driver boards the same part number for all the axes? You might be able to swap them, but there may be other reasons that this would not work. Someone really familiar with the Bandit 3 hardware would have to answer that.