One of the most common reasons a Kenmore or any other brand washer won't spin is something preventing the lid interlock switch from activating, according to RepairClinic. The problem is sometimes as simple as the lid not closing completely. Other switch problems include lint jamming in the switch or a cracked switch. Sometimes opening and closing the lid or removing lint is all the machine requires to spin again.
If the machine is overloaded, the motor circuit sometimes trips. These switches take approximately 15 minutes to cool and reset. Dividing the heavy load into two smaller loads prevents tripping this circuit. Loads that become unbalanced also have the potential of tripping the switch, according to About.com.
Although most new machines are direct drive, older ones use a belt drive. If the belt breaks, the washer no longer agitates, spins or drains. Broken belts require replacement. Some machines allow the user to tighten loose belts. Properly tensioned belts have one-half to three-fourths inches of deflection between pulleys. It is also possible for belts to develop a flat spot that allows the motor to turn without spinning the basket.
If these steps do not work, the problem is likely more serious. Motor and transmission problems with a washing machine are repairs for the pros. Owners should ask for estimates to see if replacing the unit is a more economical choice.