Well, as far as the ballast I don't think I would replace it unless it is bad. It is normal for them to get hot as they are reducing the ohms to your ignition otherwise you module would burn up.
I was speaking mostly about the car not running one time then running fine the next. I had a 72 Dodge that did something similar. It would start but when I released the key and it returned to run, it would die. In that instance the ballast in the run circuit was bad and I replaced it and was fine after that. You can test the ballast with an ohmmeter. I am not sure what your ignition needs, its usually around 8 ohms or less, I run a Unilite and it requires a little more than 7, anything more than that would burn the module in my distributor up.
Is the car starting and then dying when you release the switch, is it not turning over at all or turning over and not starting?