iPhone is plugged in, shows low battery, but won't turn on.

I had it plugged in for about an hour on my regular charging cord. It worked fine on that cord early this morning at my friend's house. I switched the cord out with a newer one to see if that would fix it. I then plugged it into my laptop to see if maybe the outlet was the issue. I can't perform a hard reset because my home button does not work. The screen is responsive and displays the low battery icon when the wake/sleep button is pressed, but it won't turn even after charging for 30+ minutes.