Its hard to say if the humming sound you hear is actually the fuel pump or the ABS brake pump running. If it is the fuel pump it should mean you have fuel at the fuel rail which would enable the engine to start if the injectors are triggered to open by the fuel injection computer, and the ignition system then ignites the fuel mixture. It is hard to say with out being able to experience the problem first hand, or be able to drive the vehicle and experience the problem and carry out some basic tests.