If you push the button in while you're trying to start it, the car will think the clutch is not depressed, and not start. If the plug is out then it will always think the clutch is pushed in and start without pushing the clutch in.

I would check elsewhere, unless the rubber thing broke and the brake lights were on all night and there wasn't enough power to start the car, which is what I would bet. Since after you jumped it the fuel pump primed. I'm going to say dead battery is at least one of your problems