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The problem you are describing does sound like a bad fuel pump. I would start with checking to see if you have 12 volts on both side of the fuel shut off switch and if so, also check it at the fuel pump with a helper cranking the engine over. The power wire at the fuel pump connector is the Pink and black. If you have cranking voltage and no fuel then the pump is bad.
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If you have 12 volts at the pump and a good ground then you are right. The pump is bad.