Here are your parts, includes a wiring layout.

I am assuming that the unit is getting 240 volts and that you also checked that it is getting the two 120 volt legs.
The motor runs off of 120.

The unit has 2 thermal fuses, both kill power to the motor.

One on the blower (Item 10 in Section 7). The most common cause of this blowing is a malfunctioning/dirty vent system.

And one on the heater (Item6 in Section 6).
If this is blown get back to us as there are other things to check and you may also have to replace the hi-limit thermostat depending on what caused it to blow.

Other things to check are the push to start switch and the door switch.

A blown heating element will not stop the unit from starting.

OOPS!! Looks like I forgot to add the link to the parts in my earlier post.
Replacement parts for MAYTAG LDE8616ACE Dryer - Ele | AppliancePartsPros.com

The hi-limit and the main control thermostat will not stop the unit from running. They just shut off the heating element.

Check the hi-limit the same as fuses.
Unplug the unit, unplug one side of the thermostat and measure it.
It should be 0 ohms.

You can also check the main temperature control thermostat this way.
I think the contacts will be the purple to red.
Note: This thermostat has a heater built into it. This is turned on for the low temperature setting. That is why it has 4 connections.

Your start for the motor circuit is:
Neutral , WH29 , DOOR SWITCH , YL35 , YL34 , PUSH TO START SWITCH , RD30 , motor's start and run windings via the centrifugal switch , GY51, THERMAL FUSE , GY25 , THERMAL FUSE (HEATER) , GY24 , timer contacts , YL43 , L1

At least that is what it looks like to me when I trace it out.