iPod Touch 4th Gen. will not turn on!

My iPod touch 4th Generation will not turn on. I've only had it since September and have barely used it. I plug it into my computer and it doesn't charge, it doesn't turn on even with a low battery symbol... my computer doesn't even recognize it as being plugged in. When I plug a 3rd generation in, it charges and is recognized by my computer, so I am almost 100% sure it's not a problem with my computer.

I've tried holding down both the home key and the power key at the same time and nothing happens...

Help please!