Try plugging the USB cable from the iPad into a computer USB port. Assuming you have a powered USB port on your computer (and you should if it is within the last few years) and leave your computer on and running (not in a sleep mode and make sure if it is a notebook, plug it into the wall). If the iPad charges then it is the AC adapter amd not the dock cable. If it does not charge, but syncs, it is eiither a bad cable or worse, a bad power controller on the iPad. The iPad (as well as iPhone and iPod) dock port had 30 pins in it. Some are for data while others are for power. I have seen the power controller go out on an iPod and not charge but still sync with a computer.
Another great way is to either get another cable and AC adapter you know to be in good working order and try different combinations if cables and adapters until you find the bum culprit. Or take it to a Apple Store and plug it into one of the display iPod, iPhone or iPad power cables.