Been there. During the last ice storm I was out for a week. We had portable dvd players for both kids that we would watch during the evening and I would take to work and charge or charge at relatives. My daughter had a Nintendo DS, also rechargeable and my son had an earlier version. We played board games, card games and read books. I also had a small b/w battery tv, so my daughter didn't go into shock from no electronics. I actually enjoyed the whole family huddled around a 9" b/w picture with the fire roaring, hot cocoa from the coleman stove.
We had a roughly similar experience after the ice storm. Our portable DVD player would just barely squeak out one movie on a charge so that was usually the last thing we did before bed in the evenings. Our kids love all their electronic gadgets but we also have a double size closet that is full of nothing but games and arts/crafts. That closet got a pretty thorough workout during that week. I even got a chance to read to the kids which was something we hadn't done much of in a while. Honestly it was just a camp out in the living room.