My SGT since yesterday also got problem, yesterday morning it auto shut down & I can't switch on it for nearly 1 hour. Then I found now the battery drain out very fast. It will suddenly drop from 30% to <15%.
Today when I charged it, it charged from 61% - 68% after almost 1 hour charging, after I unplugged & plugged the charger, it suddenly shown battery was charging up to 99%.
Is this due to software problem or hardware problem? I think it need to send back to Samsung service centre for checking. 

An owner here in our forum ( check back old thread ) had reported this problem ; he sent in and got the battery replaced as it was defective. Apparently this is a problem with some units as similarly reported in other forums too. So don't wait - get it replaced

He can get ori set with that price