when it shows "F" does it cycle through numbers and then "F"?
or does it just go to "F" and shut down?

if it cycles through numbers and then shows "F" that is low battery power.

if it just displays "F" with NO numbers cycling then that is a possible transistor failure.

Have you tried running the 'self diagnostic' on the unit?
this will cycle through all the functions of circuits and if any fail the diagnostic will halt at the point of failure during the test.

there should be a diagram under the hood that includes the self diagnostic codes and steps, just remember to jack the drive wheels off the floor and remove the drive fuse before starting the test or it will not let it start, display will show a 'd' if drive fuse is still in when you try to start the test. The drive fuse is the one closest to the capacitor or middle of truck, the middle fuse is hydraulic and the left side fuse is power steering.