When you ran out of gas, you may have damage your fuel pump. It may have overheated because there wasn't enough gas to keep it 'cool'.
This combine with the fact that you said you had to change your battery makes me think that your fuel pump had being overworking for a while before it happened resulting in the pump getting hot thus more amps got pulled through the pump circuit (possibly draining your battery).
Also, you said your fuel pump was in your trunk? It's usually inside the fuel tank and you actually have to lower the tank to access the pump.
Anyway, if there is no power to it, you may have an open somewhere in the circuit and you need a wiring diagram to help you in the troubleshooting (open relay.). It could also be that your neighbor checked for voltage when the circuit wasn't 'live'. Did he turn the key to the 'ON' position when he tested it?
A quick check: when you turn your key to the 'on' position, do you hear a slight noise from the fuel tank? If so it means your fuel pump actually turns on and put the fuel system under pressure. If not, you either have a bad fuel pump, or an electrical issue in the fuel pump circuit.
If you don't hear a noise when you turn your key to 'ON', do a fuel pressure test; it will tell you right away if you have pressure in your system when you turn the key or not.
Another trick to make sure your no start problem is due to a bad fuel pump or something else:
buy you a can of aerosol starting fluid; spray some in the throttle body while cranking your engine and if it turns on then dies after a few seconds, it means you have compression and spark but no fuel, therefore you know your fuel pump is very likely to be the problem.
Finally, does your car have an inertia fuel shut-off safety switch? If so it may need to be reset.
Good luck
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Saturday, March 6th, 2021 AT 1:09 PM