I don't know if this helps, but I experienced a similar issue with my iPad 2 after updating to iOS 7.
My "solution" to the problem, after pulling out my hair for hours, is to plug it in the wall charger, and then shut the iPad down completely. It does charge when turned off, although a bit slower than usual, or so it seems. Pheeew...
I realize that this is a pain if you have a problem with an iPhone, because you have to turn it off to charge it. Presuming that this works, of course. Otherwise, I don't know..
After the update, the iPad simply does not respond when i plug in the charger, nor does it connect to the USB port. The battery just keeps wearing down. I think it could be connected to the firmware change that iOS 7 brings, which I guess in itself has to do with Apple wanting to block out 3rd party manufacturers of power adapters of the new "lightning" type.
The only thing I can think of that might have gone wrong on my part concerning the update is that I didn't have it plugged in while installing the update - although I believe this is recommended from Apple. I'm thinking that in my case the new firmware update simply hasn't registered any adapter present upon installation, and that might have caused the iPad to not recognize an adapter at all, regardless of type. I have always used original Apple adapters, btw, so I'm not really guilty of anything other than not plugging it in while updating - or, at least that's my own theory. Which is better than no theory at all.. ;-)
Obviously, I'm waiting eagerly for Apple to solve this issue. Not really happy at all with this..