I'm just leaving this here as useful information to those who might face down a completely frozen Kindle.
Mine suddenly stopped working as I was reading some books from my childhood (Greenwich, from the Dark is Rising series.) Suddenly it didn't respond to anything, no buttons, no power down, no reboot, no light if I plugged it in to recharge. Nothing.
I called the Amazon help line, and after retrying all the things I already tried, I was told that it was just broke and out of warranty and they could send me a new one at about half price if that was okay. I said no.
But my wife noticed that the now-bricked Kindle made a slight rattle when shaken. I pried off the back cover and found two tiny loose screws. There were three screw holes, so I searched for and eventually found a third screw jammed under the Kindle mainboard. When I put these back and tightened everything, it sprung back to life. Saved myself sixty something bucks for a replacement.
The screw must have been shorting something. Was it a problem with quality control at the factory? Maybe, but I had a Kindle cover that latched these two metal probes into the side of the device, and I now realize that those two probes could have pried at the mainboard enough to force a loose screw to come even more loose. Bear this in mind if you have a Kindle go south: you might have a screw loose.