Mitsubishi Repair: My Mits Died, ground cables, battery cables

Question
I have a 95 Mits Mirage 1.5L and have been having issues with identifying what's wrong with either my battery, alternator or bad battery cables and/or fuses. I first assumed the alternator was bad, removed it an got it tested. It tested fine which lead me to believe my battery was bad. I got my battery tested an it came back as being a bad battery. After re-installing my alternator and putting in a new battery, my car seemed to have worked fine. One night I'm driving home and I noticed my interior lights were real dim and getting dimmer. Low an behold, my car cuts off on me. I got it jumped and it runs for a very short time an cuts back off again. Could my problem be a bad battery connector; positive or negative ground connections?

Answer
Lawrence,
This does sound like you have a poor ground or a short in your charging system somewhere.  You may want to replace the battery cables and connectors going from your battery to your starter.  And, be sure the connections at the alternator are secure.  Test the voltage and amperage across the battery while the car is running. Be sure to clean all your ground connections and test them with a voltmeter to be sure there is no resistance from the ground cables to the chassis.  
Good luck!