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The best option is send the Kindle to Amazon. Amazon usually don't repair or replace the screen. They usually replace the entire Kindle with a new one (if it is under warranty) or will replace it with a refurbished one for a reduced cost if it is out of warranty or of the warranty is void. To setup replacement, you have to contact Amazon. Here is the number --> +1(###) ###-####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
Call Amazon and they will arrange the shipping and send you necessary details.
Or you can send your Kindle to Mission Repair --> http://www.missionrepair.com/Amazon_Kindle_Repairs_s/1263.htm
All your purchases are saved on your Amazon account. So when you get the Kindle or when you get replacement, you can register it with your Amazon account and you will be able to redownload all your past purchases without paying again.
If you have any questions or would like any additional information, please don't hesitate to ask.