Something to be aware of is that if a device with a lithium ion battery, such as a Kindle, stays dead too long, it's designed to stay dead. Dead really means the battery is totally dead, not that the device won't start by itself. Devices will refuse to come on but can be recharged long before the battery is really totally dead.
The problem is that once the battery is truly flat connecting a charger to it can cause a fire and that's why they're designed not to let that happen.
Anyway, the advice you got above is good advice and I'd try it at least overnight before giving up. But then if it still doesn't come on you might consider replacing the battery.
My Paperwhite 2 battery was holding a charge for less than a day so I ordered a replacement battery from Ebay for $10, I think. It arrived this morning. It came with all the tools I needed. I went to Youtube and looked up a video on how to replace the battery for my particular Paperwhite. I watched it a couple of times. I started taking the Paperwhite apart.
First, it wasn't much like in the video at all although watching that video first was extremely helpful. There were enough things in common that I was able to figure out the differences. Second, that's easily the sloppiest, clumsiest and scariest thing I've ever done. And when I was a kid I used to ride in airplanes with a guy who loved flying under bridges. This was way scarier.
About half way through getting the case apart I was convinced that I simply wasn't going to be able to do it but at that point I was fairly sure I couldn't get it back together anyway so I figured I might as well keep going. I did. Everything you can imagine went wrong and yet right now my Paperwhite is charging it's new battery and working perfectly. i have no idea how I managed that. I've been an atheist most of my life. Maybe it's time for a prayer of thanks.
So, for $10 and 20 minutes of terror I now have what seems so far to be a perfectly good Paperwhite with a brand new battery.
Barry