i suggest either wipe battery status take battery out hold power button in 10 seconds let go of power then put everything back together leave the phone unplugged till dead then charge till fullest this is called fully power cycling your battery.
step 2
from there dont remove the battery you may have to do only these last 2 steps for the next 2-3 days of only fully running bat dead and leave phone to fully charge.

let us know how that worked for you .

 

from the picture below that I sacrificed one of my batteries so I could show here in this post is why we need to wipe battery stats

sounds as if we are close to resolvement though it don't seem to be that power button trick worked but if your noticing a difference from there then it worked

also you should have noticed that it behaved a lil differently when it came back on ?

also go into recovery and wipe batt stats and wipe the sys cache and also while in there wipe dalvik cache let me know how that works for ya
if you need further assistance on how to do that hit me up and Ill see if I can walk you through it with you

as for this lil chip that is on the batteries main system board is where the life span of the battery is stored and how the phone communicates with your battery. This is also how manufactures knows how and what happened to your phone when exposed to water or harsh environments