The model number does not look correct, please check it.
Kenmore models are usually all numerals XXX.XXXXXX

I am assuming that when you hit the push to start the unit is stays totally dead (no noise etc.).
Also I am assuming that you have a meter as you said the switch works.

First try flipping the breaker off/on slowly a couple times. Sometimes you can loose half the line without actually tripping the breaker and the motor uses 120 volts (one side of the line).
If this does nothing.
Measure the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the unit's terminal strip to ensure they are properly connected and none of them have burned off
If OK
Plug the unit in and check the voltage at the terminal strip. This is just in case you have a bad line cord. Be careful 240 volts is lethal.
If OK
Many units have a thermal fuse on the blower (often a white device), check this for continuity. It kills power to the motor.

If blown be sure to clean/check your vent system as this is the most common cause of it blowing. Also does not hurt to clean/check your blower wheel.

Another possibility is the door switch.