Phil;

The Ignition is not at issue here!

Symptoms you report could be caused by poor Battery charge or connections, or a poor connection at IGN Sw Terminal 50 or Solenoid Terminal 50 ...and the fact that it worked after "a few tries" is the definition of an intermittent condition somewhere...these are sometimes tricky and challenging to find, but not when guided by good troubleshooting technique...the last suspects would be the components like IGN Sw or Solenoid themselves, or even Battery, but good troubleshooting technique dictates that NOTHING is ruled out or in until its condition is confirmed.

...in order to get to the root cause, the next time it does this trick, you need to take note if the Dashboard Indicators dim during the Starting attempt (as a result of an excessive voltage drop caused by solenoid current draw) if they do, it means either the voltage drop is a result of a poorly charged Bat, or a poor connection at Bat or related (chassis, ground strap, sol) which is resulting in a voltage drop when Solenoid is attempted to be energized...and too much voltage drop, there will eventually not be sufficient voltage to get a click from sol...

...only if Dash Indicators stay fully lit and don't drop in brightness whatsoever during Starting attempts should you suspect connections at Ign Sw term 50, Sol term 50, or those components themselves...to bypass many of these and rule them out, you could simply try the old "screwdriver bridging across fat and 50 terminals at Sol"...(IN NEUTRAL PLEASE!)

Good Hunting, and please report back with findings!

PS; If you're still turning a key, that's on borrowed time too, especially with the multiple turns against the gorilla return spring which are surely occurring during your multiple Starting attempts...see: http://www.sw-em.com/swemkits.htm ...remember, key failures are fatigue failures, and fatigue is cumulative!