Door openers have a gear that drive the chain (irregardless if plastic or metal). Most gears are some sort of plastic. After time this gear wears or looses teeth. When you hear the motor running but the chain doesn't move its most likely the largest gear. (check all gears) Remove the gear and take it with you (to match size) to any Garage door opener installation shop. Usually they carry parts. For Craftsman take the gear to a Craftman Service Center. Their not cheap, perhaps $25 or 30 bucks.
But you will save the service call fee.