I really think you are fighting a really low voltage at the coil also. you should have at least 7 volts at the coil with a ballast and closer to 9. During start/crank cycle you should also see full voltage, or near 12volts when cranking the motor over, then when you let off the start it should be near 7-9 with key on.

When you had it jumped to battery and it tried to start, more than the coil, it was probably because it was seeing enough voltage to light; which leads me back to the coil being wired right or wrong.