I have a '67 SS 350. Occasionally, when turning the ignition key & trying to start the car, nothing would happen. Happened with engine hot or cold. All lights, radio, etc. would work fine, just nothing would happen when trying to start it, not even a click. Put in new battery, new starter & solenoid & still have the same problem. Probably 95% of the time it starts just fine. Will try to start it with a battery pack & sometimes that will work but sometimes it will just start without a jump after trying a few times. Car runs great other that that issue. Don't feel comfortable taking it anywhere not knowing if it will start or not. Sure could use some guidance.

 

Could be two different problems - no crank or cranks and no start.
If automatic equipped, could be neutral safety switch adjustment - select Park &/or Neutral - or NSS is faulty.

If manual trans, could be ignition switch itself.
You can temporarily set up a test light with solenoid R terminal wire so when start is selected, does light light or not.
If no light and no click, no start power from ign switch.
If light and no start, then gas problem.
Sixty-seven's need the yellow wire from R terminal to coil + terminal as ign switch has no START ign power like a '68 switch does.

Same event (no crank) happened to me and I pulled out the ign switch, undo the crimps on the end, watch out for the springs, and emery paper the contacts and reassemble.
Worked great. Also put in a marine pushbutton START switch just in case it didn't work, but did not need to use it.

 

Could be a bad ignition switch, or bad/corroded connection at the switch, or the wiring between here and there. Have you tested the start wire at the starter with a meter to see what voltage you have (or don't) when the key is in the start position?

 

I will check the NSS & ignition switch. Have not tested the start wire but I will. Do you think one of these would cause an intermittent problem?