iPhone goes from dead to turning on and then dead and turning on again.
I had just gotten home and my phone had died one our prior. I plugged it in and used for about an hour or two until it eventually went back to 100%. I put down the phone, still plugged in, and went on my computer. After approximately 30 minutes, I went to check my phone again. However, I saw that it was dead. I went to turn it back on and when I saw the white apple in the middle of the screen appear, I though for sure it was just restarting. However, the phone went to black and then back to the battery with the red sliver signifying that it was dead. Then, the white apple appeared again and the exact same thing happened over and over all while the phone was connected to a power source and charging. I tried holding down the power and home button simultaneously and did so for about a minute which stopped the cycle. However, as soon as I let go, it started again and has been doing so for approximately an hour. What can I do to fix it, getting a new phone is out of the picture.
iPhone 5, iOS 9.2