On your solenoid... the 'S' terminal gets 12v power from the start position of the ignition switch to energize the solenoid. The 'I' terminal sends full 12v power to the coil, bypassing the ignition resistor/wire during starting.
If you touch a jumper wire from the '+' terminal to the 'S' terminal (trans in neutral, wheels blocked) the solenoid should energize itself (with a solid easy to hear click), and the starter, which should turn the engine.
Like CrownVic55 said, you may have a bad ground.
If the solenoid body has a good clean connection to the truck body but will not energize try connecting a temporary ground wire from the battery '-' cable to a solenoid mounting bolt.
The lug bolt fitting end of the '-' battery cable should fasten somewhere on the block or head, not the truck body.
There should also be a heavy duty electrical 'ground' strap/wire between the body and the engine, or... sometimes another wire that's part of the '-' battery cable, that fastens to the body.
It provides a return path to the '-' terminal of the battery for everything electrical that's grounded to the body.
I suspect your body to engine wire/strap may be loose, broken or have rusty connections.
If any 'ground' connections are loose or corroded they will cause problems.
FYI, Photo, here's an alternate version of the solenoid wiring in some Fords, depending on the under-hood position of the battery and starter cables, they're just swapped side to side. The solenoid works the same either way.