having problems starting and idling, especially when it's cold outside.

My 2002 Ford Focus SE is having problems (sometimes, not all the time) starting and idling, especially when it's cold outside. I had an air flow sensor replaced and a new battery installed, but when I come to a red light, it will shake a little, like it's going to stall. Or it can take 5 or so tries before it will even start. The dealership who "fixed" it checked the alternator, starter, etc and said the only thing they could find was that one cell in the battery was dead (and replaced it). Other than having these problems when it's cold, it also seems to happen when all the electrical systems are on (lights, radio, defroster, etc). I've taken it to two different car repair places, and no one knows what's wrong with it- help me, please!