ignition/starting questions??

I have a strange situation with my '67 Fury. It has a '76 318 engine with the factory electronic ignition set up with four prong resistor. After it sits for a day or so, it requires two to three tries to start the engine. It turns over but doesn't fire until usually the third try. I have to pump the gas pedal five to six times. Today when it started, it backfired like a rifle shot. I had trouble like this a while back and discovered a poor connection at the ballast resistor.
I checked the distributor cap inside and it is fine showing no sign of cracking or carbon tracks. Once the car has started, it runs and starts fine, smooth and powerful. I know that the resistor is bypassed when starting but this seems to involve the part of the ignition that provides power while the engine is turning over. It almost seems that that phase is not functioning but when the key is released to the run part, the ignition is suddenly powered and could account for the explosion that happened. I am not familar how that works.
As I stated earlier. it only seems to occur during that first start up. Could there possibly be a problem with the module? As always, I am most gratful for any info here.
John

I'd start by pulling the yellow solenoid wire off of the starter relay to disable the starter as to not run the batt down & have a helper hold the key to "start" & you under the hood checking voltages at the ballast/coil/ECU and check the dist pickup gap (.008")

another thing to check is after its been sitting for that amount of time pull the air cleaner and check to make sure you have a good pump shot when you give it throttle..good luck..Rob

Thanks guys for the tips. I will perform these tests.
John