I might be getting to the party late, but here is my experience.

I bought my 2007 coupe in January, over the phone from a dealer in Michigan (I'm in KY). I flew up, did the paperwork, and hit the road headed home in cold, cold weather. I noticed that the cd player would stop running for a few seconds when I would turn on lights, seat warmer, anything electrical. That seemed odd and concerned me, but my override concern was to get home.

After about an hour, missed meals caught up to me and I stopped for a bite. Back in the car, the dash lit up strangely and the car refused to crank. After fooling around with it a bit, everything went dead.

I surmised that the car, which had sat unsold for over a year, including through some very cold weather lately, had suffered a weakened battery that gave out after being charged and run for an hour. It cost me a night in Findlay, Ohio, but the local dealer replaced the battery the next morning, and Monroe Dodge--where I bought my car--even paid for my motel, so I can't complain. In fact, I now have a fresh battery.

Anyway, it sounds to me as if you are experiencing the same symptons. I know it seems unlikely since your alternator should be carrying the load, but strange things do happen.

Good luck.