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Parts for Kenmore Dryer 11066914690 - AppliancePartsPros.com

If you go to the Sears parts site they have part breakdown diagrams. Unfortunately they do not share theses with other part vendors.

Do you have the wiring diagram?
if not look in the control console often it is stored in there.

I cannot find the wiring diagram for tis unit but have attached an example wiring diagram that will at least give you some info on how this series of units are wired.

The only thermostat/fuse that will effect the motor starting is the thermal fuse on the blower.

If I have attached a wiring diagram that is close (I think) the following should help you track down the problem.

Unplug the unit. Have the timer where you set it when starting the unit.
Set your meter to the most sensitive scale and short the meter leads to together so you can see if the meter has a zero offset.
Now attach one meter lead to the L1 prong on the power cord and leave it there.
Now work your way back through the start circuit.
Timer BK should be 0 ohms.
Timer BU should be 0 ohms.
Both sides of the push to start should be 0 ohms when the switch is activated.
Keep the switch activated.
Both sides of the thermal fuse should be 0 ohms.
4M on the motor should be 0 ohms.
5M should be a couple ohms (the motor windings).
Both sides of Timer Switch 4 should be a couple ohms.
Both sides of the door switch should be a couple ohms with the door closed.
Keep the door closed.
Neutral at the terminal strip and prong at the end of the power cord should be a couple ohms.

With luck you will find the correct wiring diagram so we do not have to guess how it is wired.