Suggestions from a non-expert user:

1. contact customer support
2. press power button for 40 seconds to try to reboot
3. This is not the exact same situation as you describe but it could be helpful (albeit risky if it does not work):

I had I situation where I reset the Kindle PaperWhite and something did not work. When I connected the Kindle to the PC via USB, I could see only 2 folders on the Kindle (so something clearly got corrupted). I was getting the circular loop animation but it would not stop (normally it would loop by segment until it finished loading the OS). Finally it was just a solid circle so I knew something was seriously wrong.

So, connect the Kindle to the PC via USB cable and in your file explorer open the root directory of the Kindle (say :F drive). In the root directory of your Kindle create a new EMPTY text file (using notepad) called "DO_FACTORY_RESTORE.txt"

Go to folder options to unhide known file extensions and rename the file from "DO_FACTORY_RESTORE.txt" to "DO_FACTORY_RESTORE".

Eject the Kindle from the PC and hard reset the Kindle (press the power button down for 40 seconds).

If successful, it should load up like a brand new Kindle.

If that doesn't work, I guess it is back to customer support. Good luck!