Some common causes of a Kenmore dryer not spinning include a broken drum belt and problems with the dryer's motor or with the capacitor. Broken drum belts are the most common cause of a drum failing to spin, but mechanical problems with the motor and capacitor can cause the drum to remain in place.
To determine whether the belt is in working order or is broken, open the dryer door and attempt to turn the drum manually. If the drum offers resistance and turns slowly, the belt is in working order. If the drum spins easily and freely, the belt is likely broken.
If the Kenmore dryer turns on, indicating that there is no problem with the electrical functions of the machine, the motor or the capacitor likely needs to be serviced. According to experts at Do it Yourself, "You can try checking by turning the dryer on, reaching in through the door to spin the drum by hand and closing the door again. If the dryer starts to work until it has to stop to reverse, you can be certain the problem is in the capacitor."
Kenmore dryers that need mechanical work should be serviced by an authorized technician to avoid injury or further damage to the machine.