My iPhone turned off, now it glitches on the apple restart screen?

My IPhone 5c turned off at 84%.

Now, the screen is black and it does not respond to anything unless it is plugged in. BUT! When it is plugged in, the starting white apple screen shows up.

It stays up for eight seconds (I actually counted this and it is consistently eight seconds.)

Then the screen glitches and turns black again. After the screen turns black, the phone tries to restart again. The screen also stays black for eight seconds. This repeats itself for as long as it is plugged in. What do I do??

p.s when it is not plugged in, the screen is only black and again, responds to nothing. There is not a screen that displays that the phone's battery had died. I had heard about a simillar issue but the battery thingy was on when it was not plugged in. My issue does not include that, and it does not turn on at all, really as it never gets past the white starting screen.