My wife let her Kindle Paper White's battery get so low that the screen froze. Last night she put it on charge and this morning it still had a frozen screen and it hadn't charged. Here's what you need to do if it happens to you. Fasten it to your computer. Your computer will not recognize it. Hard-boot the Kindle by holding the power button down for 20 seconds or more. Nothing appears to happen. Leave things as they are for an hour or so and it will then tell you that it is charging (with a never-seen-before screen). Again, your computer still won't recognize the fact that it's fastened to it. Leave things alone! Eventually, the Kindle will shut down properly, it will reboot, your computer will recognize it and it will start to charge normally. You don't need to "eject" it from your computer, just leave it alone and it will charge fully and then you can use it. When the battery gets SO low, it's a game of patience and I suspect the same is true of other stubborn frozen screen situations.