Your battery sounds like it's shot, too. The larger gauge charge line from alternator to battery will help with current draw (big amps, electric fans, high wattage lights, etc.), but won't (shouldn't) have any effect on voltage. A properly charging alternator will put out a minimum of 14 volts- any less, and something is wrong.
I can call AMA (think its called AAA out in the US) and have them test the battery im sure.