Well, the larger contacts are used by the starting system. They disable the starter unless the lever is in P or N. If those failed, I imagine it might cause the engine not to start, but it shouldn't cause it to die.
I will say that the mode switch is a real pain in the rump to get plugged in. I suppose it is possible that the cable is loose. I suppose you could pull the face off your computer and check that continuity is going all the way through to it.
I don't suppose it is dropping any codes?