The weirdest problem ever

A nice lady brought an iPhone 6 in today. Her phone was off, and it would only display the apple logo for about three seconds, then it would "turn off". Except I noticed the display was still on. Opened it up, and sure enough, the backlight was on. So I put it into dfu, and restored. I've seen blue screens, I've seen red screens. Never seen a salmon screen

So restore it a few more times, and then it shows the apple logo, all distorted. Like corrupted data. The phone is now constantly trying to boot itself, and finally does. Just now she emails me, says he phone is back to it old tricks. Shows apple logo, "turns off". Anybody got anything?