Solution : I'd solved this issue on my Xperia J.
What happen :
Probably it's due to heavy usage.. till the point when the battery % reaches the end.
As I put on the charger, something bad happened.
Battery reads 1% perpetually - even I charge for 2 hrs.
Worse, I can still use the phone to goggle, then it will auto shut down in a range of time.
After a while I see Battery reads 100% - happy - then auto shut & became 1% again.
What goes on , I only suspect battery died. Call Sony Center for help.
I was contemplating going to Sony or getting a new phone!
During this while, I continue using the phone (cabled) & always power ON & OFF..
Unroll I got used to it...
Something unknown happen - maybe it a shock or fracturing on the battery or a electronic reader or connection ---- I do not know -
** BUT, now let me assured you - there's nothing wrong with your phone or battery **
How I solved this problem!
Fact is now I'm using this exact Experia J with its original battery - & it works just as fine as before.
Solution: It came upon as a surprise! Because I continue using it with the charging cable - power ON & OFF ... over & over again... SUDDENLY, during one of those time when the Battery reads 100%, I decided to unplug the Charges & (a bit skeptical & unsure) ... then the phone became functioning normally. It's been a couple of week since my Xperia J became normal.