I just got caught up on this show. I disagree that six months is a long time for a society to disintegrate. You only need to look at hurricane season or something like hurricane Katrina to see that it would happen much more quickly. I have been much more surprised with how mild the scenes of the immediate post-tech world have been.
As for the batteries still working after fifteen years--I have an old Rio mp3 player from 2002 that still holds a charges enough to play for twenty to thirty minutes, and when plugged in still plays fine. I have no problem with all the electronics working for the brief amount of time they were on.