Hi @ralguy
Seems as though there might be a problem with the start circuit in the motor, either the motor start winding or the centrifugal switch in the motor.
With the dryer turned on and "humming", try turning the drum manually and then see if it continues to run by itself.
If it does then that's the problem. For the motor to start turning current has to flow through both the start and run windings to create enough magnetism to overcome the initial inertia of the motor's at rest position. When the motor gets up to speed the centrifugal switch in the motor operates and disconnects the start winding and the motor continues to run on the run winding only. The start winding is disconnected as it has only very thin wires and you don't want it to burn out, the run winding has thicker wires so that it can run for a long time.
When the motor has stopped the centrifugal switch releases and reconnects the start winding back into the circuit for the next start
Unfortunately, unless the switch is easily accessible (usually it's buried in the motor windings) you can't test which is the problem and the motor will have to be replaced.
The motor part # is WE17X10010. Search online using the part number only, to find suppliers that suit you best.
Here's the mini manual for the dryer that may help as it shows the motor windings and the centrifugal switch