Auto door locks? check fuses underhood and under rear seat if all good probably have an issue with the lefrt front door latch this would cause radio problem as well
I would look at the ignition unit. These vehicles with the timed power to radio that is supposed to cut out after a few minutes with the ignition off to prevent the battery from being run down have a timing circuit built into the ignition. That radio will shutoff when the door is opened as well so you'll also want to check the door sensors or switches. a faulty switch will prevent the auto lock from activating as Chevrolet built a delay into the system that prevents the doors from electronically locking when a door is open.
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