Hi Peter, welcome to the forum. Glad you decided to join us here at Android Tablets. Allowing the battery to totally discharge may well have damaged it, and that's very likely to be the problem. I'm moving your thread to the Bauhn Tablets forum for you, where more people familiar with that tablet are likely to join the discussion and try to help you. Good luck!
Still under warranty? Take it back if you can. I took back my wife's tablet (not a bauhn one) after nearly 12 months to KMart, got it replaced with a new and better one. The bauhn ones come with a 12 month warranty.
I personally think that it is the charger. After purchasing several new chargers and still not being able to get more than a 25% charge I decided to try one last thing before throwing mine against the wall. I plugged it into the usb port on my cable box, I got the red x over the battery charge icon then I powered it down. After about 30mins I checked back to see if it was charging and it was, very slowly might I add but it was charging. I hope this helps.
Charging via USB port works, but yes, it is at reduced capacity to the proper charge socket and power adapter. These tablets had issues with the charging system, power/volume buttons, battery, software bugs etc etc.