The fuel pump discharge check valve reveals that it is not doing its job when you have to crank the engine for several seconds before it will fire. The check valve holds pressure in the fuel rail when the engine is off and lets it start as soon as the EEC knows which cylinder is which and starts flowing fuel through the injectors and spark through the plugs.
If the fuel pump discharge check valve leaks, it will take a second or two for the fuel line pressure to pump up to normal pressure before the engine will fire. To check if that is the case, prime the pump by turning the ignition key to ON a couple times and letting the fuel pump run for the 1.5 seconds before turning the key to START. If the engine fires as soon as it starts spinning, the check valve is leaking.
The rumbling you are describing sounds like the return line "check valve" and is more of an audible annoyance than a functional problem. While you have it exposed, you should replace it. I have posted the Ford part number in the Forum before so you could search on it.