Will not start without A/T light coming on

My vehicle will not start unless the A/T light comes on. Sometimes when I am driving she shuts off and will not start. Other times if I rev the engine as she shuts off, she kick starts back on. The key has to stay in the ignition at all times or it will not go in. I do not know what the problem is. I do not have the money to take it to a shop or to have them run a diagnostic. I had the battery, alternator and starter check. Everything is good but I do need to change the battery. I just want to know what is wrong with it.