I finally found a solution to the White Screen Problem and it is surprisingly trivial. It worked on five or more HP Omnibook 500s. Theoretically, it should work also on yours. Both laptops have been working for more than a year again. One just travelled with me to Japan and Germany, agin. I originally wrote these lines looking at the screen again! For more comments and success stories look at the HP Forum
The reason for the white-screen problem is not the screen. HP just replaces the screen as a standard procedure, but the screen is usually fine. The problem lies in the HP connecter design of the screen. It allows the connectors to move slighly and therefore the contact oxidates at the connectors. That is also why it sometimes works, and sometimes not.
The procedure is quite simple. Just follow the following steps:
You should have a working laptop after that! However, I take no legal responsibility. If you damage your laptop or your health, you are on your own.