Well, I'd first suggest a software restart via the menu system. Then a hard restart (which is nearly the same thing but sometimes does things the software restart doesn't). You've tried that, so the next step would be a factory reset -- which you can also do via the menu system. But I think I'd contact Kindle CS before going there. It WILL remove all your content and personalization so it's not a step to be taken lightly.
There are links for Kindle Customer Service, by phone or email, in the FAQ sticky at the top of this section of the Board.
If it's under warranty still, they'll replace it for you if they can't help you work through a fix. Even if it's out of warranty, they might be able to help -- either replacing it at no charge, or giving a discount on a purchased replacement.