Nothing happens; not even a click. If the starter is not spinning the engine, then you should be able to hear the fender-mounted relay click. Hence the NSS diagnoses from me.
Ya know there is a definitive test; just short the big stud on the relay to the little one. If it cranks, obviously the starter is fine. If it doesn't crank nor click, then obviously the solenoid is asleep.
But if it cranks by shorting, but not by key, then the problem has to be the pull-in coil inside the relay is not receiving what it needs or it's broken. Since it is intermittent we can assume the relay is fine. Which then leads to the next logical diagnoses, that the little coil needs BOTH power from the key AND a ground at the NSS.
So jumper the ground and hit "crank". If it fails to crank, then get an additional jumper and jumper the power to the other side of the coil. If it still fails to crank, simply short the large studs together again. If it again cranks then the relay is in fact toast. But if it doesn't crank, give the solenoid a bop with a hammer. If it now cranks, Remove the power jumper to the relay, then remove the starter and clean the mounting surface so the starter clearly has a ground, and then short the studs again. If it still requires a bop from the hammer, then rebuild or replace the solenoid first. Then back to the top.
The above assumes the battery cables are clean and tight at both ends, and that the battery is in fact not dead nor damaged inside, and that the transmission is seeing the battery negative, and that the nss is on the correct roostercomb, and that battery voltage is coming from the ignition switch in crank position. Wheph.
I think I got that right...