I had the same problem, the battery had discharged to zero and the tablet would not turn on. I plugged it into the charger which I usually used.
The tablet would show the charging battery icon on the screen with a round icon then it would show the battery which would show 2 gold charge bars
then the screen would go dead and all would be repeated. When I plugged it into my PC I would get the ding dong as it was first recognised then the ding dong
again as if it was being removed. The wall chargers I was using were for HTC phones and rated as .5 amps output.
I solved the problem in the end when I plugged it into an apple iphone charger. I believe the original Samsung charger is rated at 2.1amps. I guess the
apple charger must be rated 2amps or so (The text is so small I can't read it??!!).
It seems that if the battery charge is too low the tablet can't negotiate the input from a lower power charger. Best bet is to never let the battery
charge go lower than 15% then although it will take longer the lower power chargers will work.