My iPhone 5c is stuck at 1% battery. Turns off if I unplug it, but won't increase battery. Help?

Recently my iPhone 5c iOS 8.4 died and when I finally got it turned back on to charge it, it stayed at 1%. I thought it just was a bug problem, so I unplugged it. It died. I plugged it back in to charge and it wouldn't charge. It stays on 1% battery. Does anyone have this problem? Any solutions that don't include a new phone or battery?