It seems like there is internal failure which is with the hardware.
I know it's not what you wanted to hear but I will try my best to present the "not-a-good news" in an acceptable manner.
Now, the best thing to do is contact Amazon. They will send you a replacement for free(as yours is less than a year old)
There is no point in repairing because it will cost you a new Kindle.
I would suggest, call up Amazon and get a replacement. That way, you will be able to read your old books which are still present in your Amazon account.
By the way, you can get all your books from archives so you won't lose them at all and till you get a new one, you can use your Kindle account on your computer or ipad or laptop to read the books.
You can call Amazon at 1-206-266-0927
If you have any queries, please do not hesitate to ask.
Please do not rate unless you are not satisfied. A Poor/Bad(1 or 2 Star) Rating affects my profile and performance here. If you feel like rating "Bad Service/I expected more" or "Poor Service/Helped a little", please stop yourself from rating and continue the conversation. I want you to be a happy and satisfied customer. If I have given you anything less than an excellent service, please let me know so that I can assist you further in providing the excellent service you deserve.
If you feel I have helped, please click on any of the smiley faces/stars after the second one from left to accept and rate my answer.