The ballast is needed since it allows a 6V coil to run on 12V. Chrysler did this for cold starting. When it is really cold outside the battery voltage is only 9 or 10 volts. When you draw current for the starter, this drops to 6 or 7 volts. If you have a 12V coil there isn't enough to run the ignition. With the ignition switch in the start position the ballast is out of the circuit and what voltage is available is applied to the 6V coil and you have a spark that is hot enough to fire the plugs. Once the engine has started and the ignition switch is in the run position, the ballast is in the circuit and there is 8 or 9 volts applied to the coil which works fine. Gotta love Chrysler engineering.
Check your ballast, if it reads more than 1.5 Ohms replace it. If it reads around 1 Ohm, replace the coil. Hope this helps.