Try charging it for a long time and try and turn it on. If it still don't work, try holding the home button and power button together untill you see the Apple log, then release.
have you tried plugging it into itunes, what happens, anything?
If its new, then I would go to the Apple store and get a replacment as you will still have 11 months warranty.
------------------------------Intel Core i5 750 @ 3.7GHz,
Antec 25 Kuhler 620,
Asus Maximus 3 Formula,
4GB 1333MHz Corsair, NVidia GTX 275,
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