<<<Every site shows the wrong image for 6931EL3003F
And if ordered/received---and has a *button*---it is also the *wrong* part.
This part is the HI LIMIT THERMOSTAT and is located at the 1 O'clock position on the gas burner assy.
It is also listed as M220 on the parts illustration.
Absolutely NO BUTTON should be on the HI LIMIT THERMOSTAT.
<<<Not sure where to order the right part at this stage.>>>
Try Marcone Appliance Parts
<<<I have the 6931EL3003C
I removed on my desk. I cannot get the button to click no matter the pressure I apply - do they break or does it have to be tripped by heat internally to click?>>>
The THERMAL LIMITER will only "click" if it is *tripped*.
Using a test meter---the THERMAL LIMITER can be tested for "continuity".
Of open (and will not "click" either---failed/bad).
I've never had one fail to reset.
<<<Doubting this was broken at this stage....>>>
Yes---based on your additional posts---it's clear that the gas burner is only functioning initially but not continually (intermittent).
This usually caused by the following (in most likely order):
1) Failing MAIN BOARD (6871EC1016C
) The gas valve *relay* fails after one or two burner cycles.
2) Failing GAS VALVE ASSY (5221EL2002A
) Valve 1 or Valve 2 fails after one or two burner cycles.
3) FLAME SENSOR (6501EL3001A
) Erratic operation.
4) CENTRIFUGAL SWITCH on the MOTOR (4681EL1008A
) Erratic operation.
The most common culprit on an LG gas dryer built 10 years ago---would be the relay on the Main Board.
To test---start dryer and run until burner flame no longer re-ignites (such as you've already discovered earlier).
Unplug the dryer.
Remove the front of the dryer but leave the door switch plug connected.
Set the front of the dryer off to the left (or have an assistant hold it)
Lower the top cover of the dryer.
Set the test meter to DC voltage test mode (direct current).
Pull off the plug to VALVE #1 (on the right side of the gas valve).
Place the test leads into the plug.
Plug in dryer.
Power on dryer.
Select the *Normal* cycle and press the START button.
There should be 90 volts DC at the plug.
If no voltage or less than 90 volts DC is present/shown on the meter---replace the MAIN BOARD.
NOTE: In the Service Manual---there's a *typo*.
The Service Manual for the DLG0332W dryer shows/instructs the servicer to check for 120 volts AC
at the gas valve assy plug(s).
Try this step first (several times if needed) to test the reliability of the relay on the Main Board.
If the MAIN BOARD (relay) tests good/okay---we'll move on to the next most likely component---the GAS VALVE ASSY.