If capable, unplug dryer and remove face to electric panel that holds the on / off switch and timer knob. Behing the on / off switch is a electrical contact. You may get lucky and find that this contact has overheated and welded itself shut.
If so, pull apart and file to clean the contact. Should be good to go after that.
Make sure dryer is unpluged while working on unit and do not plug back in until fully assembled.