Ok, it seems like there is internal failure which in 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, there are two options, one is contact Amazon, who might provide you discount on next purchase of Kindle and the other option is buy another E-Reader.
There is no point in repairing because it will cost you a new Kindle. Also, if it were less than a year old then Amazon would have provided you with a new one- free of cost.
I would suggest, call up Amazon and try to get a deal on another Kindle. 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.
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