Why can't I turn on my iPod?

Okay, so here's the deal. I have an iPod touch 5th gen (32gb) that I've had since August. Last week, I plugged it into an old stereo system and it happened to be almost out of battery charge at the time. So I plugged it into the charger too, and it started overheating quickly. I unplugged it from everything and turned it off, then put it by the window to cool off. Now it won't respond. It won't turn on and I've already tried rebooting it by holding the home button and the sleep/wake button for over ten seconds. I contacted a local repair store and they said they'd look at it for $25, but I'd rather try here first. I don't want to waste $25 if they can't fix it. I'm hoping it can be repaired, but I don't know anything about electronics..