Forget the battery and starter, you have a fuel leak somewhere, or clogged fuel return line.
Checking fuel pressure with a mechanical gauge would be a good starting point, and pressure should hold at 45psi for a minute or so after pump is off.
If normal pressure, raise car out on stands, pressurize fuel system by turning key to on then off and inspect entire fuel delivery system from tank to fuel rail.
Fuel leaks can sometimes not be visable on a hot engine since the gas evaporates very quickly, but this is a dangerous situation, a gas fire is a distinct possibility.
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