Broken down college kid

UPDATE: so this is what we have found so far today. We started checking voltage at the ballast and every reading we got with the multimeter checked with specs as explained above. Since the ballast is good, we went to Neg coil terminal and it read around a little over 11 volts with key in RUN position. The Pos coil terminal read roughly 9.5 volts while cranking with the key.

Is this the problem because the coil is not putting out the 10.5 volts as suggested ? If so, what would be causing this because the coil is brand new when we tested. Would it help to try and jump the car off with jumper cables ? The battery is reading a little over 12 volts as is and is cranking the engine no problem, so is this necessary.