how can i move my books to a new kindle if the old one does not work?

Make sure your new Kindle is registered to your Amazon account. Log into your Amazon account and find your Kindle library. You should be able to move your books to the new Kindle.

If you had stored the books in The Cloud that would have been easy,  but they now may be lost forever. It's always a good ideas to keep copies. 
Is it the screen not working or is the kindle completely dead?