Wow a page and a half of well-intentioned guesses and we don't even know if it turns over but won't fire, or if it doesn't even turn over, or what type of ignition system is actually in there. Now guys are talking about jumped chains lol.
Honestly 149 different things could cause the issue but we need as much information as possible or you could end up rebuilding the motor and then it still won't start. But I wouldn't feel right to just bitch and not offer any suggestions...
So does it crank okay?
If not that narrows it down a bunch. Battery/cables/connections, starter or relay, ignition switch, neutral safety switch.
If it cranks but won't start, then it gets a little more involved.
Is the carburetor actually getting fuel?
Turn the key to run and check for voltage on both sides of the ballast resistor and at coil (+).
You'd like to have 12v on the feed side of the resistor (the one wire side) and 7-10v on the other side, as well as at the coil, but as long as it's close to that it's not the problem...50+ year old wiring's likely to have a little voltage drop.
You answered a question earlier about it being points or electronic ignition with "it's been upgraded"....but from the pictures it sure looks like it's still running breaker points. This makes a big difference in the direction of troubleshooting as well. I had a neighbor sit a Chevelle in his driveway for 3 months because he didn't understand how to test and set points (chevy guy pffft).
If you can verify spark, and fuel, then you can start messing with verifying TDC and the distributor, feeling for compression and all that jazz..that could very well be the problem. I do the other tests first because they're quick and easy.