97 toy corolla. Ran out of gas. Put. 2Gal. Engine wants to start, wont turn over, mechanic says i need new brain box ecm, pls advise, got jumps still nothing

There is nothing wrong with long idling. As long as the cooling system, especially the radiator fan works properly. But it is very bad to habitually run you car very low on gas, the pump is in the tank, and running out of gas will burn up the pump, the gas is what cools it. The pump doesn't 'know' it has no fuel to pump and will keep trying. But that will not cause a no-crank issue. It will crank over, but not start. Sometimes when people say it won't crank, or won't turn over there is confusion, a lack of communication, they mean won't start. But if that is what is happening, the engine will not turn and try to start, first check your battery terminal connections for corrosion, they must be clean and tight. And if your battery is 5 years old or more, that's about the life-span of a battery, you may need a new one. Now, as for the ECU. if the mechanic says you need a new one, I can't dispute that without being at the car, he must have a reason to say so. That can cause a no-crank. But remember, keep more gas in your car or you will be in for a lot of cost that could have been prevented.