This just happened to me with my iPhone, although I threw it against the wall first. Basically if you are unable to get it out of DFU/Recovery mode using the methods listed when you google "How to get iPad out of Recovery Mode" there is likely a blown fuse on the logic board. Does the iPad get hot when you have it connected? Then this is likely the issue.
It could also be that your battery finally gave out, and it could be time for a new one. Try the methods when you google that above, and see if it works. If not, it may be destined for the shredder, and in that case I hope you had iCloud set to automatically back up everything.
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