I'd take it back to an Apple store. They can at least diagnose the problem and, in the best situation, repair or exchange it for you.
If that's not an option, I'd call Apple Tech Support for answers.
I hope this gets resolved soon - good luck!
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Ir's under warranty, so worst case you can take it to the Apple Store for repair or replacement. First, try these steps. (Apple Troubleshooting Assistant)

http://www.apple.com/support/iphone/troubleshooting/phone/
Source(s):
http://www.apple.com/support/iphone/troubleshooting/phone/

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If it isn't dead (covered under warranty) it is probable that you drained the battery completely. In that case, you won't see a thing for a while even if you plug it in. How long has it been since you plugged it in? Also, put it on AC, not on the computer.

If it has been more than an hour, then it is definitely bricked, just bring it to the store and play dumb. Don't volunteer information, simply say it stopped working and it has been plugged into AC for more than X hours with no improvement.
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One other thing you can try if you have had it plugged in for at least and hour is a hard reboot. Press the power button and home button together until you see an Apple logo on the screen. This might take a minute or two so be patient. If it doesn't cycle to the apple logo I would also recommend taking it back.

Hope this helps,
George
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