iPod touch 5g won't charge/turn on?
I just got a brand new iPod touch 5g this month for my birthday. I've had it for a little over a week and it has been working perfectly. I went on a trip to Kansas City this weekend, and used my ipod during the ride up there. It drained the battery substantially, and it must have died. When I got home to charge it, I plugged it into my computer and waited for iTunes to recognize the device, but it won't. When I try to do anything on the iPod, this image appears:
and then it vanishes after a few seconds.
When I go to turn the iPod on, it won't. And now it won't charge and the above image is the only thing that appears when I try to do anything. I've tried plugging it in and waiting for periods of time, but that didn't work. I've tried restoring it, but whenever iTunes downloads "iTunes Software Update" I get an error message when it's finished downloading.
What is wrong with the iPod? Is the battery defective? Is there a way I can fix this at home or do I have to take it in to Apple? Or is there a simple solution to this that I'm missing?
Thanks in advance.
iPod touch, iOS 6