Kenmore Elite 73942 Gas Dryer only runs with start button held

If it is winter, the air flow safety switch might be frozen by air entering the exhaust tube from outside. To check, disconnect the exhaust hose and use a heat gun to backfeed hot air into the burner manifold. This should thaw the switch vane if it is hindered by frost or ice/snow entering from the outside or left over from the last drying cycle. Note if the exhaust hose is plastic you have to use low heat on the heat gun to prevent meling the hose.

Unplug the dryer. Open the control console.Mark and remove the wires from the start switch.
Using a volt meter set for continuity,touch meter leads to R1 and R2 while pushing the switch. No reading is a bad switch.
Touch meter leads to R2 and CT1. No reading is a bad switch.
If the switch checks out good the start windings in the motor are bad.