I've never had a problem with mine starting after it gets into that same state (radio on, AC running, lights on, etc.) so I'm suspecting a lost contact with the key fob? I know it sees it initially because my lights flash when I grab the door handle to open the car.
I always have the fob in my backpack that I toss on the passenger seat so maybe it just takes a minute to re-link? Eventually after multiple presses of the start button it will fire up. It's only happened to me three times in about a month of daily driving so I'm not too worried. No vehicle is perfect!