My S3 charging is all over the map.

[AC Question]

Okay, here's how it goes. It's almost as if I have two separate phones running. First, the green battery shows almost full. I turn it on and after the banner and the blue light displays it shuts off abruptly and shows the grey battery. I have a new battery installed. Charging takes a very long time as well. I brought the phone to a local kiosk and the rep told me that a charging life of four to five hours was common and that there was nothing wrong with the phone. He then suggested I buy a charging case so that I had back up power on the fly. I'm trying to charge from my computer now. The wall charger is 1000 and not 600 and I've tried shutting down running in the background apps. Any ideas would be muchly appreciated.