Assuming that the Ignition Switch is properly operating, check the connections at the battery and the starter. Always check the most simple things first. I had the same issue with a 2001 F-250 5.4L 4x4 at the dealership, and it was all due to dirty battery terminals and a loose connection.
The 5.4L has a tendancy for the starter wire jam nuts to back off over time and cause a poor connection. Most typically it is the small ground wire, but both are prone to loosen. Also, the solenoid housing on the starter is made of a cheap plastic, and that also has a tendancy to break, leaving the stud for the wire loose from the solenoid.
Best Of Luck