My iPod touch 5g won't turn on

I bought my knew iPod just over a month ago and it has been working perfectly so far. But when I got up today and I pressed the home button, nothing happened. Normally it would come up with the lock screen so I knew something was wrong. I then tried to turn it on and it wouldn't turn on, it was just frozen on that one screen. I decided to plug it into my laptop and open iTunes but still nothing happened to my iPod. My iTunes started downloading apps from my iPod onto my laptop but it didn't come up with my iPod being synced. As my iPod is still quite new, I was understandably worried about it. Please help me get it to work

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