I experienced similar problem six months ago.
Immediately after turning the key to starting, (a) Message low level of fuel, (b) key coded correctly recognized by BCM - means padlock sign off on the panel, (c) no popping sound of the drive starter contactor after turning the key, (d) three audible tones failure alarm, (e) low level of fuel message on the display,
...and nothing happens. The starter motor not triggered.
In all cases, all returned to normal after about half hour. In the local GM dealership, using the TECH2, the expert did not identify any error on at least two occasions. When I wanted the recriate the problem, I could not. Not reproducible.
Via web search found similar reports that pointed to basically two suspects (excluding failure in ECU):
1 bad connection somewhere in the CAN network.
2 - Electrical interference generated by a relay with bad contact in the car.
I put my scanner (PC Touchscan and OBD2 adapter) in the luggage. Immediately after an event (in downtown), using my scanner I could identify registered DTC U0100 (network failure - Loss of communication ECM / PCM "A").
What did I do:
I opened all the CAN network connection points and cleaned with contact cleaner spray.
In the relays allocated by the motor box, and tambám the relay box under the dashboard, identified at least four relays that were activated immediately after turning on the ignition key. I replaced these four relays for new (two of them already had discoloration on heating (!!)).
The problem disappeared. Despite I have not specifically identified the cause of the problem, in my case, this action of relatively low cost, eliminated the problem.
I hope this can be of help.
Tazzi (please) can enlighten us something that eventually I have not noticed here.
(I join the Croewy to thank you for your always welcome clarification)