I had a similar problem with a Paperwhite recently roughly about the same time as you did. I charged by using a fast charge cord (for Fire) plugged into wall. I did a complete factory reset 7 or 8 times before it would completely reset and start. Now it works fine and has for the last 2 months. I sometimes held the button down 60 seconds in case 40 wasn't enough.
Don't waste hours of frustration. Just charge it up, put on the telly and repeatedly do factor reset (which is 40-60 seconds of holding down the on/off button). Less frustrating that way.
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