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When I hit my remote start next to my 05 250 5.4 I hear the fuel pump kick on but it has a sound first off that almost sounds like there's air in the line. The sound it hard to describe but like I said it sounds like a liquid pump that has air in the line. I wonder if this is my issue with lack of power.
I don't know if you have a returnless fuel system, but if it is a return style fuel system, air will not stay long in the fuel lines. One a returnless air could only go out the injectors, now a liquid will absorb a gas at a rate relative to it's pressure. So I suspect a couple of minutes of running a returnless the air would be absorbed into the gas.
Since the fuel pump runs a couple of seconds, I would expect a return style fuel system. You can check the pressure, but air shouldn't be stuck in the lines unless you have a leak. That leak should turn in to fuel leak at normal pressures.
I'd say try a fuel pressure leak down test. Hook up a gauge to the test port, charge the fuel system and turn the key off. Ideally the pressure should remain constant forever, but as long as it doesn't drop much over about an hour you should be in good shape.