if they have a backup have you tried to run the DFU Process? could be a software issue. How to perform a DFU: https://discussions.apple.com/thread/526...

When having issues with the battery its hard to determine if the issue is the device or the battery itself things that save the battery life are: (1) switch auto brightness on (2) checking location services so this for example is everything you have facebook or your camera app open it will always constantly try and find your location this has an affect on the battery also. (3) making sure apps are closed down in the background these are the things that affect battery life. it also could be software your running, a way to determine this is if you back up the phone first and completely wipe its contents and start from new if the battery issue improves then it could be software your running. lastly if all these fail then i would say perhaps its a hardware fault but that for me is a last resort. hope this helps !!!