From what you're describing it sounds like the motor drive coupler has failed. Please click on the link provided for testing & repair instructions covering the drive coupler replacement. Another possibility; transmission, motor or pump.
to the washer before attempting access.
Why is my Kenmore washer not agitating or spinning?
If you do not feel confident repairing this problem yourself, then you can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services
SAFETY NOTICE: Be sure to disconnect power to the appliance before performing any repairs. If you are not comfortable with doing any voltage checks that might be recommended, please contact your local service provider for repairs. Be aware that there could be sharp edges inside the appliance that could cause cuts or other injuries to yourself or others.