Actually i've found it quite peculiar that the tab 3 doesn't charge with some adapters, even if they are the same voltage output etc. For instance my blackberry charger, same size, spec etc charges the tab 3 for about 30 seconds then stops.
My theory is the converter in the original charger adapter head. I could be wrong. But if you aren't using the original usb adapter head for the tab then it might not charge properly. If you ARE using the original (i noticed you said the usb works) then maybe the adapter head is damaged some how. If so then seek a replacement charger.
If it comes down to the tab itself. There had been reports of people returning tab 3's because they wouldn't charge. And most customer service reps said they just performed a battery pull. I'm not suggesting you try to open it up but if you haven't voided the warranty, try seeking service rep's assistance and see if the battery pull does the trick.