My dryer won't start. It begins to hum and then turns off.

This sounds like the motor can't start :
Either the drum can not rotate because it is blocked (easy to check from the front, when it is empty), or the start capacitor that allows the motor to start is faulty.
In that case the motor hums, gets warm, and the thermostat cuts off.

Replacement of the start capacitor : it is not too expensive and available from every same-brand supplier and from Sears Service department (http://www.searspartsdirect.com/partsdirect/index.action)

Make sure the powercord is disconnected and on the floor in front of you, when working on the electrics of a dryer.

Success !