I had the same problem your experiencing a few years back with my 70 Satellite...

It didn't always want to start as it should and seemed like there was no power in the start location of the switch...

Occasionally you could turn it over and flip the switch back to run fast and it would fire...

It turns over just fine but never tries to start...

Mine ended up being a bad ignition switch not always supplying juice to the run 2 terminal...

Sometimes it was fine...other times it didn't start...

You can always turn the key to the run position and jump the starter relay and it will start...provided everything else is in working order...

All ignitions in my cars I've done in the past ten years I scrap everything original and run all aftermarket components...

My last 3 builds are all full MSD...

No more issues...