Unfortunately your Manage My Home profile and question did not provide a model number so it is difficult to confirm what exact design you have and what is happening.
On most openers there is a "worm gear" assembly that turns the motor drive from a horizontal direction to vertical so it can operate the sprocket and the lift/trolley components. Failures of the motor shaft itself are rare and it sounds like the sprocket is still in place so the problem most likely is a failure of the worm gears that connects the two.
Look for two shafts that meet each other at a 90 degree angle and have an assembly that looks like a long tube with grooves in them (hence the name "worm gear"). There may be a detailed drawing of the parts in your manual or online at Sears.Com that will show the assembly and how it fits together. The links at the bottom of the page have more information.
Replacing the worm gear assembly is fairly straightforward but does require disassembly of a large portion of the opener and often retiming or adjustment of the travel limits so you may want to consult a professional if you have any reservations or concerns.
There are also a few designs out there that operate a little differently. So if your opener seems to be set up differently than described here, or you have other concerns, please complete your profile with your model information and model number and resubmit a more detailed question so we have a better idea how to help.