I had a similar problem with my Nokia N9.
I was updating contacts avatars and it started to lag. Battery was at 100%. I rebooted the phone and when it turned on, the battery was at 0% and it wouldn´t charge at all.
My solution: disassembly the phone and unplug the battery for a few minutes and assembly again. PROBLEM SOLVED
You can find the tutorial here http://www.youtube.com/watch?v=mSJtUbnM46E (In russian but very graphic) It looks difficult but it is not. It is not necesary to take the silver part out.
Good luck