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Replacement parts for KENMORE 11086984100 | AppliancePartsPros.com

Sounds like the motor is shot.

Try turning the drum by hand. Should turn fairly easily. If not could be the drum is jammed for some reason. You may want to try this on a couple other dryers to get a feel for it.
If it is difficult to turn run your fingers around the back and front of the tub to machine seal. To see if something has jammed between the tub and frame (bra wires are famous for this). Be careful in case the object is something sharp.
If nothing is jammed in there you will have to open it up and find the cause.

If it rotates OK.
This may take 2 people
Open the door
Manually hold the door switch closed
Push the start button and manually rotate the drum in the correct direction.
Watch your knuckles in case it starts up.
If it does start up, odds are high that you need a new motor.

Could also be that the motor is jammed solid with lint and this is preventing the Start/Run centrifugal switch from resetting (the unit is trying to start with out the motor's start winding in circuit.