Sorry, but you can't. The Kindle is broken, so you won't be able to retrieve any data from the Kindle itself.
However, please note that your Amazon Books are stored to your account, so you can download them (including bookmarks/notes/locations) to your new Kindle. Items emailed to your Kindle can easily be found in your sent box, with the search feature. Unfortunately, you will have to hunt down books that you sideloaded yourself.
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