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My old Kindles would not work at all on USB power, even overnight, even if charge turned to green, when the batteries died.
The original Paperwhite 1 is over 16 years old. The LiPoly battery (really a cell) lasts about 4 to 10 years.
So while anything is possible, including failing Flash memory, the most likely thing is the battery. You'll need a compatible part that's not too old stock. I and others have got replacement batteries that have been poor because they are too old!
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