I use the kindle on an ipad. Great for travel- books, computer, etc all in one. If I see a book and want it NOW the kindle is great- one click and I can read it. I have a lot of stuff on there that you can just pick up and start reading- Shakespeare, ancient Greek & Roman writers, GK Chesterton, Samuel Johnson, books like that. They are often free or cost next to nothing on Amazon. However, if you have to cite books for scholarly writing the kindle is sometimes useless. I have seen many kindle books- even from academic or university presses- that do not have page numbers- only location numbers. Makes it impossible to cite specific passages from the book.
Once you've ruled out the charger itself as being the problem I'd contact Amazon. Rechargeable batteries have a finite lifespan and it's possible that yours has died. I don't know if they'd be able to offer a replacement battery for an old device but it wouldn't hurt to ask.