It looks like the condenser was compromised for what ever reason. No condenser, no spark. And changing the points was probably a good idea. It is really hard to gap a used set of points, sometimes impossible.
It is also considered an improvement of the system to add a Booster because the points will last for a long long time with a Booster and the condenser is not used with a Booster. If there should be a problem the Booster can be by passed and the ignition returned to OEM in a few minutes (unless like me you have bar backs which adds a bunch of time to the procedure, I know, recently had to do this in a shopping mall parking lot)
There are other electronic ignition systems that can be used on Airheads. Some have other added advantages but the Booster is the one I prefer (I have had a Dyna III). But I will be running the OEM system for awhile, till I get a new job.