Before you attempt to replace the push-to-start switch, I recommend checking voltage at the dryer outlet. I also recommend testing the push-to-start switch using the procedure described below. A bad door switch or thermal fuse could also keep your dryer from running. I recommend testing these components using the procedures below if necessary. I provided the wiring diagram for your dryer in the first image below.
If you have a volt/ohm meter, check the voltage supply at the wall outlet for your dryer. You should measure 240volts AC. If not, this could be your problem. An electrician would be needed to correct this type of failure. NOTE: Only conduct this test if you are confident that you can safely check the live voltage at the outlet.
The push-to-start switch completes the neutral circuit from the motor until the centrifugal switch on the motor closes to take over and maintain this neutral connection. It is rare for a push-to-start switch to go bad. To test it, you could
unplug the dryer
and disconnect the wires to the switch. Measure the resistance across the leads of the switch using a volt/ohm meter. The resistance should go from infinite resistance to near zero ohms when the button is pushed in. If the switch is bad (does not go down to near zero resistance when the button is pushed in), it will need to be replaced. To replace the switch, pull the button off the front of the switch and remove the screws that attach it to the console. If the switch is okay, reconnect it and check the other components as described below.
A loss of the neutral wiring connection through the door switch could prevent your dryer from running. To access the door switch,
unplug the dryer
and use the procedure illustrated in the left side of the second image to lift up the to panel of the dryer cabinet. You will see the wire harness connection to the door switch on the left side of the dryer. With the dryer still unplugged, a technician would normally unplug this connection and place an insulated jumper wire in the harness plug going to the console to simulate the door being closed. You may be able to conduct this test if you have the technical ability to safely access the door switch and install an insulated jumper wire (the third image below shows a typical jumper wire). NOTE: Do not attempt this procedure unless you are completely confident in your technical ability to safely complete the process. Always disconnect the dryer from electric power when accessing and working on internal components. Do not let bare portions of wire make contact with the cabinet when energized.
If you jump the door switch and the dryer runs, then the door switch will need to be replaced. NOTE: Do not leave the door switch jumped and continue to operate the dryer. This is an important safety feature of the unit. Replace the door switch before returning the dryer to service.
If the door switch is not the problem, you could have a blown thermal fuse that is preventing the dryer from running. The illustration on the right side of the second image below shows the location of the thermal fuse on a similar model of dryer. To access and check the thermal fuse,
unplug the dryer
and remove the back panel. The normal way to test the thermal fuse is to remove the wires and measure the resistance across the leads of the fuse with a volt/ohm meter. You should measure near zero ohms of resistance across the fuse. If you measure infinite resistance, the thermal fuse is blown and will need to be replaced. You could jump the thermal fuse temporarily in the same manner as described for the door switch to test for motor run using the same precautions as above.
If all of the above components are okay, you could have a wiring problem or a bad motor. A technician would normally be needed to diagnose and repair this type of failure.