This morning when we first started the first drying load of cloth, the dryer
didn't want to start.

Here is your parts breakdown
Model TEDX640EQ1

Here is a tech sheet (wiring diagram) This is for an EQO, could not find EQ1. Should be close.
https://www.servicematters.com/d...0Sheet%20-%203401728.pdf

First flip your breaker off/on slowly a couple times. Sometimes half the line can drop out without tripping the breaker.

Do you have a meter?

Next would be the thermal fuse.
I believe it is Item 23 in Section 3

If you do not have a meter, you can short the two wires together, tape them up to ensure they do not short to the frame and give it a try.
If it runs, order and replace the fuse. Do not run the unit unattended with the short. This is a fire safety device!!!

Make sure to unplug the machine before working on it.
240 Volts KILLS!!!

The most common cause of this fuse blowing is low air flow so if it is the fuse clean and check your vent system.