First check to see if full battery voltage is even 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
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.
To replace the distributor follow this procedure;
The ignition timing is not adjusted with a timing light or with the engine running, and to set the ignition timing follow these procedures.
There is a mark or notch on the distributor housing that the rotor should be pointing to when the engine is on top dead center. This "static" timing is all that matters and the computer will be able to control the timing as long as the ignition rotor is in that position when the engine is at top dead center.
1. With the engine at top dead center.
2. Look under the distributor cap and find where the number one terminal runs under the distributor cap, and where that position on the distributor cap corresponds with the distributor housing, and it should match up to a mark or a notch on the distributor housing indicating the number one position.
3. With the engine on top dead center the ignition rotor should be pointing to the number one mark or notch that is on the distributor housing, Then make a reference mark of the position that the ignition rotor is pointing to (out on the engine or firewall) and the more precise you mark the position, the easier the installation of the new distributor will be. This will be reference mark #1.
4. Remove the distributor lock down bolt, (the lock down clamp will most likely be attached to the distributor and if so it should not be removed from the distributor) then slowly lift up on the distributor about three inches and note the direction that the ignition rotor turns, and when the ignition rotor stops turning then mark the position that the ignition rotor is pointing to (out on the engine or firewall) and then lift the distributor striaght up and out, and remove the gasket or any left over gasket material from the intake manifold. The more precise you mark the position the easier it will be to install the new distributor and an assistant might be helpful. This will be reference mark #2
Once the distributor has been removed it is important that the engine does not get cranked over by the starter or the crankshaft turned at all, or the reference marks will become useless.
Be sure that the new distributor is complete with a new module and that there is a new gasket in place on the distributor.
1. Lower the distributor with gasket down into the distrbutor well and align the ignition rotor with the #2 reference mark and when the distributor gear engages the drive gear on the camshaft then the ignition rotor should turn to the #1 reference mark as the distributor sets all the way back down flush on the intake manifold.
2. Install and tighten the lock down bolt, and If the distributor is properly installed then the ignition rotor should be pointing to the #1 reference mark and the #1 position on the distributor housing with the engine on top dead center.
Replace the distributor cap and connect the spark plug wires, and see if the engine will start, if the engine does start and the check engine light does not come on (assuming that it was not on before) then the distributor is properly installed and there is no further timing requirements.
Let me know if you require any further assistance.