I've cracked open my Kindle Oasis and diagnosed the problem to be a bad power switch. The Oasis won't turn on unless I go through a convoluted process of plugging it into a power source, opening the kindle cover. There's now way to shut the kindle off, besides closing the cover.
If I could get my hands on one of those power buttons, I could swap it out, and most of my problems would go away.
I suppose I could harvest a replacement power button by finding somebody's used Kindle Oasis, and scavenging the parts off of that.