new ballast resistor died in 10 minutes

The Vreg circuit is independent of the ignition, other than both get power from the key switch. Changing one thing at a time is always smart. If Vreg didn't work, your battery wouldn't stay charged.

To trouble-shoot the ballast, measure the voltage at coil+ (w/ blk lead on BATT-). The ballast should drop it from BATT+ to ~8 V when running. If you have a dual ballast, you also need to check the wire going to the ECU, but it should also be a bit less than BATT+. Insure your ECU has a good ground to the case (a rusty screw isn't).