I have a 2003 f150 heritage. the other day I was running around , stopped 3 or 4 times with no problems. then I came out of a store and no start. Nothing lots of power but not even a click. So long story short I had it towed home. I have checked battery and all connections. checked fuses and relays. I went under truck and found when key is turned to start position there is no power at solenoid. So I made a hot wire and touched to the small wire on starter. Nothing. If I touch it on the big side the starter will spin but still won't engage.
It sounds like the solenoid is not engaging. Since the starter seems to spin fine, the power and ground are probably fine. You jumped a hot wire to the starter and that had effect. That is nearly absolute confirmation that you have a bad solenoid.
The one odd thing you noted is that there is no power to the solenoid when the key is turned to the "crank" position. This could be because the solenoid is shorted rather than open. But it is strange.
Can you disconnect the "small" wire and see if it has power when the key is turned to "crank" or "start" while the regular wire is NOT attached. If no power at that loose wire .... you may have a further short or ground in ???alarm system, relays, fuses, ignition switch, etc??? hard to say, but this is not likely.
This is the most likely: Now try your Hot wire to the "small" terminal again with no other wires connected. If you still have no function, replace the solenoid and get back to work.
If it is still strange ... post some more results and we will see what we can do.