There is the possibility that the ignition coil is faulty and first check to see if full battery voltage is getting to the "Pos" (+) positive side of the ignition coil when the key is in the "Run" position, and also that full battery voltage is getting through the "Pos" (+) or positive side of the ignition coil and over to the distributor ignition module, dis-connect the wire connector from the ignition module and if battery voltage is not present at the connector to the ignition module with the key in the "Run" position but it is present at the "Pos" side of the ignition coil, then the ignition coil is faulty. If battery voltage is present then check the ohms between the high tension terminal (where the coil wire goes on the ignition coil) and the "Pos" terminal on the ignition coil by first dis-connecting the wires from the ignition coil and then test with the "Neg" lead from the ohm meter in the high tension terminal on the ignition coil, and the "Pos" lead from the ohm meter to the the "Pos" terminal on the ignition coil, and the ohm reading should be between 6,000 and 30,000 ohms and if not replace the ignition coil. A faulty ignition coil can also damage the ignition module.
The ignition module and the pick-up coil/stator located inside of the distributor is what generates the signal that the ECM (Engine Control Module) uses to time and fire the fuel injectors, as well as the signal to run the fuel pump and the dwell signal timing to fire the ignition coil, and a faulty ignition module can cause any one of these systems to malfunction.
That does sound like a malfunction with the ignition module inside of the distributor, and you can remove the ignition module and have it tested for free at most auto part stores. If the ignition module does test out alright then the problem could still be in the pick-up coil/stator, (it can be tested using an ohm meter by dis-connecting the wire connector from the pick-up coil/stator and the ohm reading between the two wires from the pick-up coil/stator should be between 500 and 1500 ohm's, and both of the wires from the pick-up coil/stator should show an open loop or an infinite reading between each wire and ground) and if the pick-up coil/stator is found to be faulty then replace the entire distributor, or the distributor will have to be dis-assembled to install a new pick-up coil/stator.
If you do purchase a new ignition module be sure that it does come with a silicone grease or a die-electric compound because it is a heat sink and the ignition module will burn up without it.
To install the new ignition module first clean out the mounting surface inside of the distributor. Then completely coat the metal contact surface under the ignition module with a thick coat the silicone grease or die-electric compound and do not leave any of the metal contact surface of the ignition module un-coated with the silicone grease or die-electric compound, and be very careful not to over-tighten the ignition module or it will be damaged.
The same principal applies to HEI
(High Energy Ignition) ignition systems with the ignition coil mounted in the top of the distributor cap.