A:
I had the same problem with a Samsung Galaxy player in the 5 inch model. What caused the problem with my battery was that I accidentally charged it with another Samsung branded phone charger (not the one it came with). Using the wrong charger did something to the battery and it would not take a charge when I tried charging it with the oem charger.
When I took it back to Bestbuy it was after a year had already gone past, so my one year warranty was gone. I was told that I would have to send it to Samsung for them to fix it. I think I remember that they also told me that even if it was still under warranty I would have had to send it to Samsung myself.
I did some research and found out that if you remove the battery it should reset the device so that the battery will than take a charge once reinstalled in the device. Many people said they tried this with their devices and it worked, however, my player had a non-removable battery. I even took it apart to look it over to see if there was any way to unhook the power from the battery. The power ribbon was very delicate and I was sure I would ruin it if I messed with it.
So I put it back together and ran the battery down as far as it would go until it would just auto shut down and I tossed it in a drawer and figured it was a write off. I couldn't afford to have Samsung fix it for me.
A few months went by and I wondered if the battery had bled off enough power to reset the device. When I plugged it in it said it was charging, but unlike before it actually started building up a charge on the battery. It has worked ever since that day, and I make sure to only charge it with the charger that came with it.