Try to do a hard reset (menu button and center button together for 5sec) while having it plugged into a wall charger. Try different types of chargers. If all that fails you have a broken logic board.
It's not too hard to replace the logic board yourself. Here is an iPod Repair Guide that shows how to open an iPod nano. Logic boards are easily available on Ebay. If you want somebody else to do it for you go to iPad Repair
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