I've had a similar problem the first week i had my powerbook. I would use the pb on battery, then at night plug it in, seeing teh green light go on, then head off to bed. Wake up the next morning and find out that my battery is completely drained, and the charging light is not on. Unplug it from the powerbook, then plug it back in...nothing happens. I had to physically unplug the power adapter from the wall and plug it back in to get it to charge.
That happened twice in the first week...hasn't happened again since.