I would check your ignition switch, Ford is known for it to expand and it lets several contacts not connect as they should. Also check all of your grounds. If you want to go thru my build thread, I show where all of the grounds are. I also show where the Ignition Switch is at the bottom of the steering column. You just remove your sterring column cover to access it. I also show how you could fix your switch.
You will only here your pump run for a few seconds as it builds up pressure but it does run all the time. Of all the cars and trucks I have worked on thru the years, I have only had two that had bad computers. I think one was a Toyota and one on a Chevy. They just are not a high failure point from my experience.
If it just a noisey pump, check your fuel filter, filters need changed a lot more often then recommended. I have seen qutie a few times where truck runs, but at low speed as they just cant get enough fuel flow. Last week we changed the fuel filter on my sons motorcycle and what a difference it made on it. If you replace the fuel filter, try to blow thru it, you may not be able to as the filter element gets a waxy build up on it. Disassemble the fuel filter the old fuel filter and you will see what I am talking about and it will convince you to change them more often then recommended.