Classic/Antique Car Repair: Electrical problem., 1967 mustang, petronix

Question
I am a student at the University of Mississippi. I drive a 1967 Mustang, she has a 289 with 302 heads and a pretty strong cam. The distributer is a Petronix. She had been running fine (as far as classic cars go) until I left the running lights on one night. The next morning, the battery was dead, so I used my jumpbox to start her up.  As I was driving down the highway to recharge the battery, she shut off with no warning and wouldn't start up for about 5 minutes.  This continued occuring about every minute until I made it back to a gas station and parked it.  Ever since it has been doing the same thing, only not nearly as often. Everytime I start her up I have to use the jumpbox. It seems like my battery isn't charging. I put a new alternator on her about a week ago. Any suggestions on what might be wrong?

Answer
Hi Trent:
Once a battery is completely drained, it sometime will develop a "Dead Cell". The fact that it cut off while driving, leads me to believe you have the ignition switch wire to the battery. It does sound like you have a bad ignition. So, if this is a maint-free battery, replace it. If it has a place for water, check it and add distilled or bottled water if it is low or dry. If this does not help, a new battery maybe needed.