Top part of agitator skipping
If the bottom agitates and not the top, the problem is likely the 4 "agitator dogs" designed to allow the top agitator to turn only one way.
This assumes that you have a basic Kenmore / Whirlpool top load, direct drive, neutral drain (it doesn't spin until the pump removes most of the water) machine.
First, see the Sears parts site for your washer:
Enter your model number (###.######) and you'll see a list of major sub-components with diagrams and parts.
Look at the section on the Sears site for Agitator, basket and tub.
See the part "Dog, agitator "
Remove the fabric softener unit, lift the top agitator cap (use a screwdriver) and you should see a plastic part in the center of the top agitator with a 1/2" square drive.
Remove the drive and lift off the top agitator. Turning it over you should see the 4 "dogs", replace these and the top agitator should turn in one direction only.
Replace the 1/2" drive, the cap and fabric softener unit and the top agitator should work.
Also see the following.