Won't spin in agitate, spin or rinse cycles - Kenmore Washing Machines

This sounds like it could be one of two things:

The lid switch doesn't work or the coupling from the motor to the transmission is broken. are you mech. inclined, as this isn't hard to do?

following is a set of steps to disassemble the machine to get to the part:

1. Using a Phillips screwdriver, remove the screw from each side of the console.
2. Pull the console forward and up to remove the tabs on the bottom of the end caps, out of the holes in the top.
3. Lift the console up and lay it on its back.
4. Unplug the harness connectorfor the lid switch.
5. Insert a flat screwdriver into the front edge of the clip (located on both sides), and pry back. Remove both clips from the holes in the cabinet and slide down the other end of the clips and out the slot in the rear panel.
6. Open and hold the lid while grabbing the cabinet front opening. Be sure when tilting the cabinet that the back edge clears the vacuum break.
7. Tilt the top of the cabinet toward you by pulling on the lid and opening of the cabinet. This releases the back slots of the cabinet from the tabs in the back of the base.
8. Carefully pull the cabinet away from the base of the washer and set it aside.
   Now you have access to most of the parts.

If you need to replace the switch, you will see it on the underside of the cabinet. Two screws hold this in place, with a retainer. Remove the screws and replace the unit. assemble in reverse order.

If you need to change the coupling, following are it's instructions

Now you see the pump on the front of the machine. Remove the clips there, and pull the pump straight forward. Same for motor, place a hand firmly under the motor as it will drop out once the clips are removed. On the back side of the motor, you will see three pronged retainer on motor and transmission shaft. When you buy a replacement for this, it will come with new ones if these are broken. Place the rubber onto the three pronged retainer, replace motor onto transmission and reconnect.

Reassemble in reverse order

Hope this helps