The only things that will stop working after the battery has died are the functions that require long range RF, such as ride photos and the interactive features on Haunted Mansion, Small World, and whatever else has some kind of display that pulls info from your account for attraction customization. For ride photos, many of the older rides still have touchpoints that you can use to add your ride photos at the end of the ride. However, Seven Dwarfs Mine Train and Frozen Ever After do not have touch points, so if your battery has died you will not be able to get those ride photos. I believe you will also miss out on the ride video for Tower of Terror.