Here is the wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%208528192.pdf

What have you tried and how have you checked the various components?

When you push the start button does it make any noise?

Since the light goes on you have the voltage to run the motor.

Best and safest way to check components is with a meter.

The most common cause of your problem is a blown thermal fuse.
This is usually mounted on the blower assembly.

Unplug the unit and check the fuse with a meter should be 0 ohms.

Jiggery Pokery method is.
Unplug the unit.
Remove both wires from the fuse, short them together and tape them up so they will not short to the frame.
Plug the unit in and give it a try.

If blown, replace the fuse ASAP as it is a critical safety device re: prevents lint fires which can turn into house fires.

Also clean/check your vent system and the blower as these are the most common causes of it blowing.

Next would be the push-to-start switch and then the door switch.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.