Here are your parts includes a wiring diagram
Replacement parts for MAYTAG MDE8057AYW | AppliancePartsPros.com

I am assuming the unit will not re-start.

First flip your breaker off/on slowly a couple times. Sometimes you can loose half the line without tripping the breaker.
Better yet check it with a meter
L1 to L2 should be 240 volts AC
L1 to Neutral and l2 to Neutral both should be 120 Volts AC

Note that if the interior light still works the power for the motor is probably OK. If the light is on with the door open, push and hold the door switch. If the light goes off, keep holding the switch closed and try to start it. This will check if the door switch is being activated, note that it does not totally rule out the switch as the cause as it's normally open contacts may be toast.

The door switch is a likely cause.
Also the push to start switch
Another cause at the top of the list is a thermal fuse Item 11 in Section 5 or Item 10 in Section 6. The one on the blower is most likely.

Unplug the unit, remove one wire from the fuse and check it with a meter should be 0 ohms.
The other method is:
Unplug the unit
Short the two wires going to the fuse together and tape them up so they cannot short to anything.
Plug the unit in and give it a try.
If the fuse is blown replace it ASAP as it is a critical safety device.

If the fuse is blown be sure to clean/check your vent system as this is the most common cause of it going.

Also not a bad idea to clean the interior including the blower wheel.
I would also check the belt, rollers, glides etc while the unit is opened up.