My iPod touch 5 gen won't turn on, but my home button is broken

iPod Touch 5GEN 16GB iOS (whatever the most recent one is, like 9.0.2 or something)

I have had my iPod for about a year and a half now, and haven't had any issues, other than my home button breaking. However, today, I was using my iPod as I usually do, and turned it off. When I went to turn it back on, nothing happened. It was at 3/4 battery. I have attempted to let it rest and to leave it plugged in, and nothing has helped. Is there anyway to fix it at home, or do I need to take it in to an Apple Store (not my preferred method, as I am a broke college student.)?