HDX won't turn off, display looks wierd

My 4th generation HDX 8.9 won't turn off. The screen is frozen, the power button won't respond, and the screen has developed strange electronic type symbols that almost look like pieces of a circuit board (not sure quite how to describe it). The battery is fully charged, as I charged it last night.

A couple of weeks ago it did something similar, except that when I tried to turn it off to charge it, the screen went black and a red line appeared on the horizontal bottom. I thought it was toast, but after about 3 days, the line disappeared and I was able to charge it and use it again until today.

These are most likely indicative of the same cause, but what? I'm not sure where to go from here.