your solenoid is bad, OR the thick wire from the battery to solenoid is bad or loose OR the thick battery from the solenoid to the starter is loose or bad.
you already tested for 12v at the tab, now test the post that is connected to the battery, there should be 12v there all the time. If there isn't the battery post, wire or solenoid post is the culprit, loosen, clean and retighten the wire and test again, if it is still bad replace the wire.
Now once you find 12v at the battery to solenoid post, test the other post while the key is in the start position, if there is not 12v at that post replace te solenoid. If there is 12v at that post test for 12v at the starter, if there is not 12v on the starter post while the key is in the start position then the wire or connection to the posts is bad, loosen, clean retighten, test again, if still no 12v at the starter post then replace the wire between the solenoid and the starter.
If there is 12v at the starter post and the starter does not turn or even try to turn, replace the started.
All the solenoid is is a switch, when 12v is applied to the tab it connects the two big posts together, thus connecting the battery to the starter, since you said you can jump the battery to the strter and it spins, chances are a wire is loose, corroded betwen contacts or the solenoid is bad.