Most likely it's something to do with battery. First try to long reset it as described here:
https://www.amazonforum.com/s/questi...zen-on-archive
I woke up mine that way once the battery was left drained for a few months. Jailbroken, but just for custom fonts in menus and in reader. It's still working right now, but I'm getting a feeling that battery won't hold forever. Battery life is still extremely long, so that's not a proper indication of its health. It takes a very long time to fully charge to 100% and green light. I instead charge it to around 95%, and I try to remember to charge it up before it's fully drained. Battery indicator is a bit iffy as well. It doesn't work quite as it used to. Sometime I'll go fast from 50% to empty, sometime it'll feel like it's on 90% forever.
There's plenty of 4 gen Kindle battery replacement tutorials on youtoube, and teardown doesn't appear to be particularly difficult, so that would be my choice. Finding the right battery might be a problem, though. And it could be also something else that failed.