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Probably the sensors are bad and need replaced, a professional scanner should be able to check them.
Possible wheel bearings, just a guess!
That will be very hard to find for the period of time it takes to duplicate, my opinion is to stay off the pedal, and save gas.
Let me set this straight, the latch is the piece that holds the door shut, so are you talking about the exterior handle may be the issue. If so it could be a bad handle or the linkage and plastic clip may be the problem.
When you turn the key, nothing - the starter doesn't even turn or engine turns and no start.
I like the Dura Max GM
Brakes locked or wheel bearing I would guess.
It's the lock cylinder, and it turns the ignition switch.
Consider the oil pump tube when removing. It will hang on the gasket, and remove the oil level sensor before removing the pan.
It will probably have to be scanned with a professional scan tool to find the issue.