The problem is now solved.
To recap, for anyone else who encounters the same problem I had:
1) Backup your ebooks somewhere. (I use calibre.)
2) Do a reset. (This will wipe off all of your content. See step #1.)
3) Register you Kindle to the same account you already have.
4) If you had Collections prior to the reset, the Collections will still exist in the Cloud. If you want to recreate the same Collection name on your Kindle, then you will first have to delete the Collection from the Cloud. You'll then be able to create a Collection with the same name you had prior to the reset. (My own personal work strategy: I no longer download my ebooks directly from Amazon. I download the ebook onto my computer and run it through calibre. I THEN put the ebook onto my Kindle. Everything on my Kindle comes from calibre.)
5) Put your books back on the Kindle. (I use calibre for everything.)
Thank you to everyone who provided advice and information. 