First thing you need to look at are the door springs. They are usually directly above the door. You probably have a broken spring and this may be the cause of your drive gear going bad.

When the door is disengaged it works perfectly fine. None of the springs are broken.

The chain is probably out of sync with the door. Remove the chain from the sprocket and run the opener until the sprocket turns counterclockwise and stops. Then with the door in the open position replace the chain. You will have to reset your limits.