2002 SL2 Stall followed by no start/power

I have a 2002 SL2 which has started developing a hard to track down problem. The first time I experienced it, I was driving at night on a cold night (~10 degrees F). It stalled after running fine for approx. 15 - 30 minutes with no real warning signs. It stalled when I depressed the clutch when approaching a stop. I noticed the lights dim and hit the starter. The engine wouldn't turn over. I turned off the lights, and hit it again. The motor turned over and started. I drove it home with no more problems. I assumed it was the end of life for the factory battery, so I purchased and installed a new battery. Skip forward a week and a half with no problems. Again I am driving at night, almost exactly same temperature, and same scenario. But this time, when it stalls everything is dead, like the battery is removed from the car. No lights and the starter would not even click when I try to turn it over. I did notice a very faint glow on the Cruise Control LED. The car is dead, so I put it in neutral and push it to the curb. My daughter jumped out, and I tell her to get back in before she gets run over by traffic. When her door slams all the power is back on! I assume I have a loose connection. I checked the battery cables... I checked the ring terminal on the fusebox., but it was tight. I looked at the body ground lug, and it looked ok too. So I am confused... the symptoms seem to indicate the whole car was starved for battery power but I can't find the problem yet. The only other information that might factor in is that I changed the starter twice on this vehicle. I changed it back in July 2006. Any ideas where to look?