I know this flies in the face of the "parts cannon" approach to repairs that most guys will give you, but here goes.
Get out your digital multi meter and when this happens, with the key "on" check for voltage at the plus side of the coil primary. If no voltage, start checking back to the ballast resistor and back to the ignition switch from there.
If you have voltage, key off, unplug the distributor and check resistance (ohms) between the two terminals on the distributor side. You should have 150-900 ohms resistance between those two connections. If you have more, the pickup is shot.
You can check the coil by disconnecting the wires and checking resistance across the primary. You should have about .75 ohms resistance there. Check resistance from either primary terminal to the center and you should have 10,000 ohms resistance or so. Those are really generic readings... and not for specific coils... and it can be argued that it's not the best test in the world, so don't discount that it might still be the coil even if those two readings are OK.
My money is on the distributor pick up or the coil.... That is assuming that this is an electrical problem and you checked and there was no spark.
Whoever told you about the 5 pin/ 4 pin deal... Stop listening to any advice they give you.