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It is possible that the battery has failed or it could be a firmware glitch. First we can can soft-reset the Kindle and see if it works or not. Press and hold down (or slide) the Power button for 20 seconds and this will reset the Kindle. Then check if you are able to charge it.
If it is not working, then connect it to your computer and reset it while connected. Then keep it connected for 20 minutes. Does it charge from your computer ?
If it is still not charging, then you have to send it to Amazon. Amazon doesn't repair the Kindle. They usually replace the Kindle with a new one. You will get a free replacement since it is under warranty. To setup replacement, you have to contact Amazon. Here is the number --> +1(###) ###-####/strong> or this number --> 1800 3000 9009
You can also contact them from here --> https://www.amazon.com/gp/help/contact-us/general-questions.html?skip=true#b
Don't send it to third party repair shops because that will void free replacement warranty. You should send it to Amazon. Call Amazon and they will arrange the shipping and send you necessary details.
Good news is, everything you have purchased are stored on your Amazon account in cloud. When you get a new Kindle, all you have to do is register it with the same Amazon account you used on your old Kindle and everything you purchased can be redownloaded without paying again.
If you have any questions or would like any additional information, please don't hesitate to ask.