Most dryers have a relay that 'latches' when you press the button to hold the circuit on. They do give trouble but simple replacement needed. Not sure of your dryer but you may need to replace the circuit board it is on.
Martyg
January 2016
my husband has changed the starter button and still the dryer wil not work. The dryer starts when you press it but does not continue when you let go of the button? can you help?