[Marshall V. Daut]

Sometimes screwing the ignition cable into the distributor too far shorts out the ignition system. The lower plate tang is pushed against the condenser and shorts out the ignition. Screw the cable in as far as it will go without forcing it, and then back it out one turn. See if that helps.
Before you do that, though, unscrew the ignition cable completely and with the ignition key ON, touch the end of the cable against a head stud nut. It should spark. If it doesn't, trace the wiring back at the terminal box to the instrument panel to find out why. Until you get spark at the ignition cable, the best distributor in the world with points or electronic ignition will not fire. If you do have spark when touching the cable, but none at the points, the trouble lies in the connection between the lower and upper plates or a bad condenser. This is assuming you have cleaned the points.
If you have spark at the cable end and at the points, but the engine still won't start, remove each spark plug and lay it on the cylinder head. Re-attach the brass plug connectors between the plugs and the plastic distributor body. With the ignition key ON, hand crank the engine so that each cylinder "fires". There should be a spark between each spark plug's electrode when that cylinder "fires" in the standard 1-2-4-3 firing order. If one or more plug doesn't fire, switch them around and test again. If the lack of spark travels with the plug, that plug is bad. If it doesn't, then the plastic distributor body probably has an internal crack. This will especially manifest itself in high humid or rainy conditions. Repo distributor bodies from the late 1980's and early 1990's were notorious for internal cracks, even when brand-new. Try a different body.
When you checked the spark from the coil, did you hold the end of the coil wire 1/4" away from a head stud nut? A bright flame should jump across between them. If not, trace back to the coil and to the ammeter to ensure connections are good and the coil has juice.
If all of these tests result in the engine still not starting, the ignition system is probably not at fault and I would take a second look at the fuel system. Remove each plug and spray some starter fluid into the cylinders. Replace the plugs and attempt to start the engine. It should start and run for at least a couple seconds. If it doesn't continue to run on its own after the starter fluid has been used up, the problem lies in the fuel system.
But work out the electrical issues first.
Marshall