Sound like maybe your ballast resistor has failed. The old points system used a ballast resistor to reduce the voltage across the points to keep them from burning up too fast. The wear pattern would be excess metal on one point contact and a matching depression on the other point contact.
That wear pattern throws the timing off and cause the engine to run rough or not at all.
It looks like
this and is usually mounted on the firewall, although I have seen them hanging off the coil, off the distributor and other locations (all bad ideas - the resistor is very subject to failure due to vibration - which is why they mounted it on the firewall.)
If you have an ohmeter, it should be about 1.5 ohms or so. If you have a voltmeter, you should see the voltage to the points drop once the engine is started. The purpose of the ballast resistor is to reduce the voltage to the coil's primary side (and therefore to the points as well) to reduce wear and tear on the points. High voltage sparks tend to melt the metal on the points, causing the transfer from one point contact to the other.
