Here are your parts
Replacement parts for WHIRLPOOL TEDS680EQ2 | AppliancePartsPros.com

Here is your wiring diagram, see attachment.
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When the start button is pressed the start contacts fire and wont fire again unles the door is open which indicates they are being latched on. The motor doesn't run or even hum.[/COLOR]
Sorry but I do not understand what you mean by "fire".

[COLOR="DarkRed"]I assume the two 12 ga. red wires but would rather be sure. checked heater and heater over temps all reads good. checked temp cycle switch and it is closed.[/COLOR]
The heater circuit is separate from the motor start circuit.
The heater runs off of the full line, 240 volts (L1 to L2)
The motor runs off half the line, 120 volts (Neutral to L1).

If the unit has an interior light.
If yes, is it still working?
If it is not then you probably have a power problem.
Try flipping the breaker off/on slowly a couple times. It is not uncommon to loose half the line without actually tripping the breaker.

If it is working then the thermal fuse on the blower assembly is the most likely culprit.
If it is blown replace it ASAP as it is a critical safety device.
Also clean/check your vent system as it is the most common cause of it blowing.

[COLOR="DarkRed"]The bulb is out but it has been blown for awhile, I will check voltage to it.[/COLOR]
It will be OK, you have already measured it L1-4
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I am not sure where the non resettable thermal limit 196F is located.[/COLOR]
Should be on the blower, Item 7 in Section 3)

[COLOR="DarkRed"]The component in the blower duct with 4 wires attached seems to be a cycling thermostat.[/COLOR]
Yes, that is correct.

It was the thermal limit ( 1" lg by 1/4" wide white with a 1/4" faston tab on each end) mounted on the blower enclosure. not sure why it failed but it has been working since the original post without a problem. $10.00 part 20 minute repair.