I bought the book on line and can't find it on my kindle

no you did not buy it from this help forum .
This assumption is very ANNOYING !
suggest you read the information below on how to buy kindle books on line
http://www.wikihow.com/Buy-Books-for-Your-Kindle

Connect your previous Kindle to computer via USB, and you will find a new hard drive in "My Computer". Open the drive, use windows search function to find your files, next copy them into your computer. ... If your books are not bought from amazon, you can sync your kindle booksfrom kindle to another one easily.

How can I transfer books from one Kindle to another Kindle? - Quora

https://www.quora.com/How-can-I-transfer-books-from-one-Kindle-to-another-Kindle Can transfer my books from one kindle to another Google Search

How do I cancel an order for a kindle book - Amazon Kindle

We don't repair anything. We only try to help people with their questions. Not knowing where you live, not even the country, makes it even difficult to help you find a certified repair centre. But perhaps you even have to think twice before you let anything repair. When the kindles are still under warranty, no problem, but sometimes the work alone costs more then a new Kindle. The best you can do is clear with Amazon what you can do with the books you bought on a Kindle, when the device is beyond repair. when you can put them on another device, perhaps it is cheaper to buy a new.

Amazon com Help

Check fixit, to see how repairs go.
Kindle Tablet Repair

Hi,

I assume you mean kindle books you order online (not from the kindle itself?)

They are delivered to your Kindle based on what you have registered on line, not to your email. Therefore changing your email address should not matter (at least directly).

When you say 'moved' - do you mean moved house physically (which does not matter at all) or moved to using a new kindle? Assuming you mean a new kindle, you need to
A) make sure the kindle is registered to your Amazon account: go to home screen, touch top of screen to bring up menu and then press the 'three lines button', select settings. There should be option to register (you will need email address and password - so you need to make sure your online Amazon account has correct email address registered! This is where email change might be causing problems, but can be updated online)

B) when you order books online you need to select the correct kindle to deliver to in the drop down box next to the order button (it might be called something like "Paul's Second kindle")

You can access all books you have ever bought (for this kindle or any other) on Kindle paper white by selecting 'cloud' when on the list of books at home screen.

Hope that helps, if not please reply and explain in more detail what you are doing and what happens / does not happen

If you bought them from Amazon they will auto restore once you sign back in.

It seems it needs repaired.
Take it to the store where you bought for service help.

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Unfortunately not - books for Kindle must be bought seperately