Ok, this is a crazy idea... but it's an idea.
How are the pins in the USB ports? The reason I ask is because my own Jasper sometimes doesn't like to boot if I've left the controller plugged in to charge and is literally doing exactly the same as what you describe and show in the video. If I unplug the controller, turn the console off and back on, it then boots firs glitch.
So yeah... like I said, crazy idea but I'm wondering if there could be a problem on the USB ports, or something is pulling too much power...