Motor Shield Not Working

I recently bought an arduino motor shield r3 for a robot I wanted to build. For some reason, I'm not sure if it's the motor shield or the motor, but one of the DC motors I'm controlling for the wheels won't run. The reason I think it's the motor shield is because when I engage both channel a and b, only b lights up. Although, it does seem like channel a is very dimly flickering when it is engaged.

Based on the situation, do you think it's the motor or the motor shield? And, I don't have the budget to get another motor shield(I know they're cheap), so if it is the motor shield can you find me a reasonable solution?

Thanks in advance

What happens if you engage only one channel or the other?

What happens if you put power directly to the possibly faulty motor from a battery?

What happens if you change the motor wiring so that the motors are on the other channels?

I'm sorry for not providing more details.

If I engage the faulty channel, a, the robot does not move. If I only engage b, the same thing happens as does when I engage both.

I honestly haven't tried putting power directly to the possibly faulty motor.

Ah, I totally forgot about that. I have rewired it, but I forgot the results. Let me rewire it again, and I'll update this post when I'm done.

EDIT
When I was rewiring my DC motors, one of the wires on the motors that had come pre attached fell off.

Thanks for the help