My name is Peter. I am a retired field service appliance technician.
After review of your washer components, there is a strong possibility that you have a bad electronic control board. You have two control boards, one is for the motor and one for the other functions.
Washer electronic control board for Kenmore Elite Washer model #11021062001 Electronic control board 8571359 is the circuit board that manages the washer's functions, such as filling, washing, draining and spinning. It sends voltage to the drive motor and other electro-mechanical component.
If you elect to replace the board make sure you ground yourself by rubbing your hands on something that is bare steel. Static electricity will knock a board out.
All appliances with electric control boards should have a surge protector. You can purchase a wall socket surge protector for $20-25.00. It is a good investment considering how expensive control boards are.
Rule of thumb; "If the unit is either 7 years old or the cost of repair is 1/3 or more of the original price, purchase a new unit.
Consider it purchasing a new unit, stripping your existing unit for parts to sell on e-bay. You will make a little money and save others expensive parts cost.