I have a kenmore model #82380100 Model Super Duty 88 that will not agitate. All else works on the machine, just won't agitate.

Check the coupler between the motor and transmission

The coupler looks OK

Have you checked the belts? Does it make a smell, like hot rubber? Our belt went bad on ours, but it made a smell because the motor was turning and the belt was slipping on the pulley. That made the transmission mess up, locked. I believe they have an anti lock mechanism on the bottom like on the garbage disposer that you can back off and reset it. At least that is what it looked like when the repairman came. Charged us 157 dollars which really was awful. We have decided we don't like repairmen much. If your agitator is locked, depending on how old your machine is. I just get a new one. The way the charges are now, you'll be money ahead...