You show a 5v connection between the motor shield and the board.
Post the details of your motor shield (link).
That 5v i suspect is an output from the motor board, have you measured the voltage on it.
In your second diagram the + supply is connected to ground on the mega and the - supply is connected to another ground on the mega.
You have probably blown a ground track off the mega.
HellenT:
I connect the 12V plug cable to the screw terminal connector of the motor driver. Then I connect a jumper from that same screw terminal to the Vin and GND for Arduino Mega.
That is not what your diagram shows.
If by Vin of the Mega you mean the barrel connector then you have the jack supplying 5 v to the mega and also the motor board supplying 5v to the mega also, bad idea.