The starting fluid and codes confirm it isn't getting fuel. You indicated there was a new key and it was programmed and recognized. Is the antitheft light staying on solid or flashing? If it is, I want you to try this. Turn the key to the run position and allow it to sit for approximately ten minutes. If the light turns off, see if it will start.
As far as the codes are concerned, P1625 is specific to the theft deterrent signal. Here is how it works. The theft deterrent module (TDM) produces the theft deterrent fuel enable password when the ignition is "on" and the proper transponder key value is detected. The powertrain control module (PCM) monitors the fuel enable password. If the proper signal is present on the serial data circuit, the PCM enables the fuel delivery in order to allow the engine to start. If the signal isn't recognized or received, it shuts down fuel.
As far as diagnosing this code (P1626), I attached the diagnostics below. (Pics 1-4) However, since you have had things replaced and programmed, I don't feel this is the issue. I believe it is a short on the GMLAN serial data circuit preventing the control module operation.
First, try the key on test. If that does nothing, go through the diagnostics below in pics 1 to 4. If that doesn't help, we need to check the GMLAN and the serial data wiring between the body control module and the powertrain control module. There are two wires in particular to check. One is tan and the other is tan with a black tracer. Confirm there is a good connection at the BCM logic module, no corrosion, and no damage to the wiring. Also, we need to check the dark green wires between the anti-theft module and the logic module. See the last pic below
Let me know if that helps or what you find.
See pics below.
Images (Click to make bigger)
Tuesday, September 13th, 2022 AT 8:34 PM