** The timer on my Kenmore dryer model 110.86583710) stopped advancing in all cycles. The dryer runs after I press the start button but won’t stop running until I move the timer knob to an “off” position or open the door. I just replaced the timer (part #694716) and the problem is not fixed. **
That symptom might be caused by a stuck ‘push to start’ button but your model also has an electronic ‘dryness control’ (see the following link) which feeds power to the timer motor and if defective might also cause such a symptom.
Kenmore 110.86583710 Electronic Control
LINK > http://www.appliance411.com/data.php?rc=2072
** … timer stopped advancing in all cycles. Is there a thermostat that can keep the timer from advancing? **
On models which use such a set up, a failure of a thermostat would usually only affect the timer on an ‘auto’ or ‘permanent press’ cycle not a regular ‘timed’ cycle so I would think a thermostat problem is not the problem in your case.
JMO
Dan O.
http://www.Appliance411.com/?ref411=Kenmore+Dryer
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