i just went thru the same thing with a f150.
-checked battery - ok, 12.37 volts
-checked solenoid - ok (very easy test, go to the web - youtube and search for 'how to test your solenoid - this will test your battery, solenoid and starter as i understand it).
-checked the voltage i was getting at the starter - from my tester put positive wire on positive terminal of starter and ground the negative wire on the frame and was getting the same voltage as at the battery - 12. 37. volts. did not crank the engine.
as it turned out, my problem was the $17 starter switch in the column. replaced it and turned the key once and it started.
starter will have 12 volts on standby from the battery at all times, its the signal wire or circuit from the keyswitch that enguages the starter.