My wife closed one of our garage doors on our child's toy.

If I unhook the garage door from the chain and close it half way the
garage door stays in that position so the springs are good. If I re-
hook the garage door while in this position and try to close/open the
door with the motor it does so just fine until it either closes or
opens all the way; at this point the motor starts grinding and
rattling loudly and won't stop until I push door button.

If I start with the garage door hooked in the fully open position the
motor will start the noise and the garage door won't move.

If I start the garage door hooked in the fully closed position the
garage door will open just fine until it hits the fully open position
in which the motor starts making the noise.

I unhooked the the garage door and left it fully closed and then
tested the movement of the chain without the garage door attached and
it moved fully from end to end without any problems.

I hope I exhausted all possibilities and gave enough information to
garner some insight.