HI Allen.
The only way to start a car with a dead battery is to get a jump start from another automobile, or use a battery charger that has an option to start a car.
No way, no time, no where, do you want to hook up a 120V system directly to your automobile. It will fry every electrical component in your car, any may be even YOU.
The cheapest solution, IMO, is to take the dead battery to an auto parts store and they can test it, and most likely sell you a new one. My experience with 12V batteries is that they work or they don't. This summer I drove to the Post Office. I came out of the PO and tried to start the car, and it wouldn't even click the starter solenoid.