Try giving it a reset. Hold down the sleep and home keys, past when you see the red power down slider and until you see the silver apple. Let it reboot and try again.
But if that charger works just fine with your other iPad and not this one, I'd call up your local apple store and make an appointment so they can look at it. Usually when an iPad wont' charge (when plugged into the wall with its supplied charger) it's
bad power brick
and if the charger is working with another iPad then that rules that out and the thing left is something wrong with the 30 pin port on the iPad, or perhaps something with the battery or software that monitors the battery. ANd things like that are beyond a user fix.
On the upside if the device is still under warranty - and barring any obvious signs of abuse or neglect - then it should be covered under the warranty.