Mine is like this too. It will not charge on a PC's USB port, and on most a/c USB bricks it will show the "not charging" symbol. I have pretty much decided this tab needs more than the standard USB 2.0 amperage (3amp) to charge properly. It will charge with most large a/c converters, but will often show the "Not charging" icon - it is charging, but slower than normal. My compact brick from my Gnex and GSIII will charge my Tab 7.7 about 50-75% overnight. My truck 4.5a converter will charge at almost normal speed, but shows the "not charging" icon. My PC will maintain charge, but I am not sure if it is adding to the charge.
FWIW-