If you think your Kindle has a problem, it is easy to set up a return for it. Just go into your "orders" section and click on the "return or replace item" button to the right of the Kindle. If you mark it as not working, the return postage will be free. Just print out the return authorization and place it inside the box with the Kindle, and print out the return postage page and tape that to the outside of the package.
There is a time limit on returns, so don't wait too long. However, I would definitely check out the Kindle forum and the live help telephone line tomorrow if you have time. Just in case it's a simple problem. With my extremely limited knowledge of electronics, it does sound to me as if your Kindle has a defect and should be returned.