Okay, so the problem is pretty simple: Prove that in a stationary (non-rotating) system, that the sum of the torque equals zero. My solution is to take a meter stick that's mass is evenly distributed. Find the center of the meter stick, then balance it on a fulcrum point. Since the object is not rotating, the sum of the torques must equal zero. Move the meter stick to the left or right, and the stick will rotate counter/clockwise. My question is, would that convince you that the sum of the torque equals zero in a stationary system?