Fuel pump, crank no start

P0037 HO2S12 Heater Control Circuit Low Voltage
P0057 HO2S Heater Control Circuit Low (Bank 2 Sensor 2)
P0261 - Cylinder 1 Injector Circuit Low
P0264 - Cylinder 2 Injector Circuit Low
P0267 - Cylinder 3 Injector Circuit Low
P0270 - Cylinder 4 Injector Circuit Low
P0458 - Evaporative Emission Purge Solenoid Control Circuit Open
P0646 - A/C Clutch Relay Control Circuit Low
P2176 Throttle Actuator Control System - Idle Position Not Learned
U2105 - Loss communication with ECM
U2107 - Lost Communications with Body Control System (BCM)

The first nine fault codes shouldn't prevent the engine from starting. Most of them likely set due to the underlying problem, and will not need any attention.

The "Lost communications" fault codes point to a failed Body Computer, but there's two things to try first. Check the three fuses with the blue arrows pointing to them. If they're all okay, disconnect the negative battery cable for a few minutes. Even better, when it's disconnected, touch the negative cable to the positive one to insure all the computers' memory circuits are fully-discharged. Reconnect the cable, then see if the engine starts.

How did you perform those tests? To check for a ground, the test light's clip has to be on the battery's positive post, then the light will light up when you probe a point that is grounded. I suspect you found places that will check to ground. We know there aren't going to be three separate problems develop all at the same time. Also, if there was something shorted on one of those circuits, that fuse would have blown.

What you're doing is powering up those circuits with the current that is flowing through the test light. The light dims once the capacitors in the driver circuits inside the various computers charge up. You're seeing the same current surges that often cause fuses to blow for "no reason" when the disconnected battery is reconnected.

Everything points to a failed Body Computer.

First I'd disconnect the negative battery cable to see if the Body Computer has locked up. We jump to defective computers too quickly and blame them for everything, but there was such a case in the early 1990's, and GM did have a lot of Engine Computer problems in the late 1980's to mid 1990's. Disconnecting the battery did temporarily solve a lot of those problems, which is why we became accustomed to doing that. It's less of a problem today, but it's something simple we don't want to overlook.

Body Computer.

The alternative is to use a scanner to look at what the computers are seeing and responding to. That will let you command the computers to do things such as turn relays on and off. That will show if they can control them.

Shame on me. I thought I posted the location already. Sorry, but it appears I did not.

It's listed as "behind the upper right side of the instrument panel".