Bill, you said it's a 69. Does it have a starter relay on the inner fender?
If so, that is where I would start my diagnostics. It is easy to get to, a likely culprit, cheap and easy to replace.
Grab a volt meter and have a helper hit the starter switch. Check for current coming into and out of the relay.
No power into the relay, continue troubleshooting toward the ignition switch.
Power into the relay, but no power out, easy fix.
Power out of the relay, trouble shoot your wiring to the solenoid. You already know the solenoid is good, it started with the remote starter switch.
And yes, the nuetral safety switch may well be your culprit. I have only dealt with manual trans, or else found the trouble to be the relay on my auto trans vehicles.
Good luck.
