I currently have the same problem on the same series Kenmore Washer. I found out that it is known part that fails that causes this, that is a pretty simple repair. The motor coupling has probably failed. This is a coupling that goes between the transmission and the motor. You can buy them on line from Sears for $15 or at repair shops for between $19 and $25. If you go to these websites it will show you how to change http://www.applianceaid.com/procedures.html#coupling. The part number you will probably be looking for is: 285753A . Check out the how to remove your cabinet and to remove and replace the motor coupling. Should be a fairly easy task, if you have easy access to the machine. Hope this helps...
Wayne
March 2007