I actually have this same model here at home for personal use and had a similar issue with charging. Googling the issue wasn't very helpful as there are tons of suggestions and possible problems and fixes.
I would start by holding the Home and power button down to enter a repair mode to see if that helps first.
Then check your charging port for debris to make sure it is not clogged up with lint, etc... using fine tweezers or toothpick (With it powered off) and be gentle as to not bend or damage the connectors (Magnification is helpful). Next, make sure your charger is working properly and cable is not damaged...then, the software, you can try restoring it back to factory defaults (You will lose data...back up first).
If none of these work, it could be a hardware issue or battery issue where you could need a charging port replaced or battery replaced.
Post back the steps you try and the results and any questions you may have. If uncertain on how to do something, ask first and someone here will be happy to help.
My issue was a bad battery :)
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