I have a kenmore top load washer, The top part of

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.

First, see the Sears parts site for your washer:
http://www.searspartsdirect.com/partsdirect/index.action

Enter your model number (###.######) and you'll see a list of major sub-components with diagrams and parts.

The top section of a two part agitator is designed to turn only one way. If the "agitator dogs" in it are worn, it wont agitate either way.

Look at the section on the Sears site for Agitator, basket and tub.

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 on how to do it.

http://www.american-appliance.com/catalog/newsdesk_info.php?newsPath=16&newsdesk_id=136