Car starts and idles roughly, press gas let go then stalls

I was driving back home the other day and everything seemed fine. Out of nowhere on a stop my car began to shake then it just turned off and would not turn back on. I was able to make it crank when I turned the key but no luck on getting it started so I had it get towed home.

My brother and I worked on it, and we change the air temperature sensor but there was no luck. Today we cleaned the throttle body and the idle air control valve (did not replace them) and still no luck.

The car starts when it is cold and stays on idle with the idle rpm's moving up and down from 800-650 which makes the idle a bit rough. That was not happening before. So the car will be on when it is on idle, but once I press the gas pedal and then let my foot off the gas pedal the car engine will shake then turn off. I can turn the car back on and keep the gas pedal pressed (revving it) and the car will not turn off, but as soon as I let go of the gas then the car engine stalls. No check engine light is on. Anyone have an idea of what it could be or what it is?

GX model, MFI CNG SOHC.