The dryer will only stay on if you continue to hold down on the start button. Is the start button the problem or is there some other issue?
Here are your parts
http://www.appliancepartspros.com/partsearch/modelsearch.aspx?model=110.64992300
See the attachment for your tech sheet.
I am assuming that if you hold the start button the unit runs and has heat.
You will see in the wiring diagram that there is a relay in parallel with the start switch, perhaps it is blown and not closing.
They are in the control console.
I believe that the motor and the heat relays are the same but double check this.
If they are unplug the unit and swap the relays.
Then plug it in and give it a try. If it now runs when the atart is released but you have no heat then you need a new relay.
AP3037419
Be sure to unplug the unit when working on it!!!