fuel pump is a good call but I think it sounds like a bad crank sensor.... if you turn the ignition key to the on position you should here a little motor turn on under the back seat. that noise is the fuel pump coming up to pressure. turn the key on and off a few times to make sure. the only way to check the crank sensor. is inspection. or replacement. there not very much. and easy. the bad news is if it's the timing belt inside the engine.
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