Ignition woes

It's not the ballast resistor. If it were, the engine would fire with the key in the "Start" position and die as soon as the key is released to the "Run" position. This problem is opposite that.

The ballast resistor is bypassed during cranking by wire J3, a 14-gauge brown wire connected to the "output" or "downstream" side of the ballast resistor. The other end of this wire connects to IGN2 on the ignition switch, which is live only during cranking. The purpose of this ballast bypass is to send full line voltage (already dropped by the starter motor draw) to the coil for a rapid startup. Sounds like you're not getting power to the coil during cranking, but if the engine happens to be at the right point in rotation on a cylinder when you release the key, it'll catch and run just before it quits turning. You've got a fault somewhere in J3; keep in mind it goes through the notorious bulkhead disconnect (at cavity Q). Rather than do unpleasant diagnostic surgery, it will be easier to run a new wire from the large terminal on the starter relay or the small terminal on the starter over to the coil (+) terminal. This will do exactly the same thing as the factory ballast bypass circuit: shoot full line voltage to the coil during cranking. If nothing else, you can throw on a quick test wire in this location to see if the car starts.