Sounds like the star-shaped thing you talk about is the chopper wheel that triggers the ignition brain.

There are 2 other "points" underneath that trigger the FI brain. They live in a little tray you can pull out. While we're on the topic, remove the 2 tiny screws that hold it in and slide the tray out. Clean the contacts with heavy paper like a business card. If there's oil in there, clean it up and start thinking where it's coming from. If the distributor seal is shot, you will have to clean those points preiodically. But in any event, they make the injectors fire, which does not sound like your symptom.

Anyway, do you know what ignition system you have? Common to Volvos are Crane, Pertronix, and Allison. Some models have an internal ballast resistor, and some coils do, too. What color is your coil? I think it's the Bosch blue coil that has an internal resistor. Are you getting any spark at all? Could be that the coil's bad, or the lead from the coil to the distributor cap is bad.

Anyway, hope some of that drivel helps.