That definitely sounds like a bad battery. Was it any colder than normal when this happened the first time? My last 323 (also e46) did the same thing when I was 3 hours away from home. I was confused too by the blinking b/c you woul think if the battery was bad then the lights wouldn't flash, but they do. Try to jump start it since a roll start isnt possible with the auto, then bring it straight to a shop and have a new batt put in. It should be fine after that. Keep in mind that your battery is about 4-5 years old now and they hold less juice as time goes on. Good luck.
Oh yeah, welcome to UB