Rapid battrery drain even after new phone/new iOS

[SFbay]

iPhone 4S battery started draining rapidly out of the blue and can't find the source of the problem. Have tried:
-turning off all iCloud/mail/sync settings
-closed out all active apps
-Apple Store reset phone and reinstalled iOS
-got phone replaced, restored to backup

...and still no change. It stops if I turn off cellular data so maybe a corrupt program that keeps getting reinstalled when I restore to backup?
HELP!!!

 

[Mrbobb]

Restore phone to factory, just enable the essentials for now, THEN reload Apps one-by-one. Painful, but that's all I have for u, unless there is a processor usage analyzer out there that can log who's the culprit.