Q: Iphone 5 has no sign of life but shows up on itunes

Earlier today, I powered off my iphone while it still had a great amount of battery life and tried to power it back on but got no response. I thought maybe it could be a battery problem, but still after a good charge time, the iphone remained unresponsive. I tried EVERY troubleshooting method, but nothing powered on the LCD, or gave me a sign that the phone had life. I plugged the iphone into the computer, and it shows up on itunes, but still has no on screen activity. I even turned the phone off and on while it was still connected to the computer, but the only thing I got was it showing up on itunes and going away when I turned it off. If anyone knows how to fix it, or what possible solutions I could have, please let me know. And also, the iphone came back on showing the dead battery screen once when I connected it to the computer, but I unplugged it to see if it would work disconnected, and after the flashing charger dissappeared, the problem occured again.