Thank you for trying,
that unfortunately confirms an internal hardware failure, and the kindle will need to be replaced.
They are not designed to be repaired economically and for most models it costs less to buy new than to repair: http://amzn.to/2fPnyHM
In that event, your best recourse will be to contact Amazon kindle service directly, at 866\321\8851. Even if past the warranty, Amazon usually has very good customer service, and will often offer a credit/trade in toward a new or refurbished kindle model.
When you receive your replacement kindle, once it is registered and connected to wifi, all of your existing books/purchases will sync to the new kindle, so you won’t lose any of the content you’ve previously purchased.
My apologies for the news.
If you have any other questions, just let me know. Otherwise, please take a moment to rate my service as this is the only way I am credited for my time. Hopefully I have earned 5 Stars but if not please let me know what I can do to ensure you are satisfied. I also invite you to contact me directly with any future support needs at http://bit.ly/1QwLxGh and ask for Nathan.
Thank you, ***** ***** a nice day,