An underlying problem you have is clear back where I asked you to check some voltages. You have a LOT of voltage drop to the "key side" of the ballast. What this means is, with only 4 or so volts at the coil, IF YOU are cranking the engine by jumpering the start relay, you will get LESS than 4V at the coil.
If you have not done so, try temporarily jumpering right from coil + to battery and see what that does.
In other words you may have two problems---low voltage, and an ignition problem. "May"
