Take your volt meter and measure voltage at the IGN side with the key ON. You should have "around" 12V. Then measure the coil side. No voltage = bad ballast. You should have "some voltage" since it is a resistor, it will not be 12V, it will be maybe 8-9? Maybe Del will chime in, but no voltage means the resistor is bad. The reason it will run with the starter engaged is because the system is wired to bypass the resistor while cranking and give a full 12V so then the ignition sees voltage and then does not when you release the key.
