If you said this correctly, then both I and 67Dart273 are confused. Doesn't this prove that the Pertronix II works and that the problem is that your key is not supplying +12 V ignition power to Coil+ (and Pertronix II). With Pertronix II, you should bypass the ballast resistor. The other possibility is that the spark doesn't pass thru the distributor correctly (phasing problem?) so it only works if you come straight off the coil.
There was a post a few weeks ago about a Pertronix I no start. However, I would treat any of these conclusions that "Pertronix was bad" as "hear-say" or "chatter" since reverting back to points could have done other things like wiggled bad wires, fixed an erratic ground, etc. Until you find root cause using a multi-meter and spark tester, there is no conclusion. One guy's metric was simply "engine doesn't run" = "spark is bad", or maybe not.
At this point, I would pull the distributor out and spin it by hand while you resolve the problem, rather than waste your battery and overheat your starter cranking the engine.
