Dryer runs as long as you hold switch

Check the door lock switch to see if it is working. Or possibly something called the relay which would be likely more expensive part to replace.

check here for fixes , it has diagrams to look at so you know what your looking for check the switch itself first http://www.partselect.com/dryer+dryer-wont-start+repair.htm

check the start button, if it runs with a jumper, the switch is bad

You most likely have a faulty motor centrifugal switch. This switch is engaged when the motor starts rotating. The switch itself could be faulty or the inertia-mechanism that activates the switch could be faulty. The inertia-mechanism usually has two small springs that pull it back into its resting position when the motor stops turning. I have found that the springs will sometimes break and produce the symptom you have described.

Below is a diagram of common centrifugal switches. The switch will be mounted on the end of the motor.

The motor centrifugal switch is not switching from the start winding to the run winding. The switch should stay in the run winding when the motor picks up speed unless power to the motor is interrupted or cut off. The switch is replaceable on most dryer models but sometimes it is an integral or built-in part of the dryer motor and failure of the switch requires the replacement of the motor. Indicate the exact model number of the dryer for more accurate troubleshooting and repair advice.

hate to be the bearer of bad news but it sounds like ur motor is going out. Had this happen to my last dryer. If this is the case it will eventually just stop. Try running it without any laundry in it. if this works, then load it and see if it still works. (poor little motor has to work a bit harder with a full load) good luck.

sound more like a control board failure // if it has one,, maybe the belt, starting switch

replace the switch...onthejob

The start button starts the motor heater and energizes a relay that latches closed to keep the motor and heater running untill the timer switch or door switch cut the power to the relay and the relay opens.
The latching relay has failed or disconnected
if all the cables are attached to the relay
replace relay
not an expensive item, good for another 10years

there is a centrifugal switch on the dryer motor. pressing start energizes the start winding and the motor runs. when the motor is up to proper rpm the start switch is supposed to kick out and the motor runs on its run winding.