I have Kindle Paperwhite 7th Gen running for last 5.5 yrs. And I had exactly the same problem as shown in the youtube video posted.
I opened the kindle, knowing ultimately I may have to throw it. When nothing worked after spending hours I tried a weird thing - took a small piece of metal and touched across the inside housings etc. suddenly all lights switched on and it started to reboot. It worked for me, and may work for some other as well - so I thought to post. By no means it is a professional advice.
I do not the know the reason why this happened but I got it fixed a weird way.
I would suggest to not let your kindle drain completely - atleast this is what happened for my device so I guess not letting it drain completely will keep it safe for longer.