Are you sure the plug is wired properly. If someone accidentally pulled a wire from the harness and they didn't know where it went, they may have plugged it back into the wrong slot. From the owner's manual, it appears that the red, yellow and black should be all together on one end of the plug. Maybe someone here has a plug they can photograph and post.
Have you checked the voltage on the plug where the wires go into the plug?
The display lights may be wired directly to the illumination wire. If that's the case, I'd suspect that the red wire was in the slot for the illumination wire.
A lot of the older units had the illumination of the keys independently controlled by a seperate wire, that's what we are talking about. Could you take a picture of the plug and post it here? Its also possible that the circuit for the constant (yellow) wire isn't connecting to the board somehow or has a bad diode in series with the circuit on the board, or even a tiny fuse or bad trace. (this is if the red wire is in the correct position and not illumination, though)
I was made aware that often the flat cable that connects between the HU and display that carries all signals often fails and breaks the connection between the two. If this is the case the display would not be able to turn the HU on?