You need a capacitor (or condenser) in the circuit across the points to form a resonant circuit against the inductance of the coil primary. Sort of how a shock absorber works against the cars springs.

Usually it's mounted on the points plate under the rotor but sometimes was moved to the outside of the distributor on dual point units.

The car may start without the capacitor, but will chew points up at a ferocious rate. Without the capacitor when the points open a good portion of the stored energy in the coil will try to jump the point gap, lessening the energy left for the plugs.

That said grab a multi-meter that has at least an OHMs and VOLTs range. With the ignition off measure the ballast resistor - it should read 0.5 - 1.2 Ohms. This sets your running current to the coil primary.

Check the points visually, do they open and close? With the wire lifted between the coil and the distributor measure the resistance between the post on the distributor and the block. Open and close the points with a screwdriver tip or by rotating the distributor housing. The readings should alternate between zero and infinity (a bunch).

Connect the wires back up. Change to the volts range on the meter (be sure otherwise you'll let the magic smoke out of the meter). Turn the ignition switch to the RUN position. You should be able to measure +12V or so at one end of the ballast resistor, and maybe +3V at the other when the points are closed. Open the points and the voltages should both be +12V.

There should be a wire that bypasses the ballast resistor during starting. This allows more current to flow into the coil primary when starting, a time when the battery voltage drops down to +7V or so. If this is suspect then you can add a small wire across the ballast resistor, just don't leave the ignition switch on for very long in this condition or you'll kill the ignition coil.

Pull the high tension wire off the distributor (center) which comes from the coil. Slip a single plug into the wire end and lay it against the block. Have someone crank the engine while you watch for spark.

If you have spark then move to the distributor cap, rotor, plugs, and plug wires. All have been replaced I assume?

Has the distributor been pulled since it last ran, was it re-installed correctly?

Regards, Mark