First things to check then are battery voltage into the unit - needs to be 11V or better. Put a meter on the crank input to the starter and see if controller is sending the crank command after the glow plug time has expired. I not certain how long the preheat is on this unit but at -5 it would be at least 15 seconds. Do you hear any relay click from controller indicating it may be trying to engage the starter after 15-20 seconds? It should also be sending power to the throttle actuator at the same time it engages the starter. This is a PWM signal so not specific voltage but you should see something between about 4 and 12V on a DC meter.
If you are getting the throttle output, you could remove the crank wire from the starter and manually activate the starter with a jumper wire to start it and see where that gets you. Like bypassing controls to start any diesel engine though, have the air intake accessible and some plywood handy to completely block the intake in case you need to shut it down quickly.
Had one other thought... If someone had installed the control switch backward it may explain what you see. Holding the switch in STOP for 2 seconds energizes the fuel pump for as long as the switch is held but would never pre-heat or crank. Have you tried holding the switch in the other position?
Good data CM. Please keep it coming.
I take it you wrench on these for a living..... either that or you are an insomniac that likes reading up on generators even more than I do
Rgds, D.