Ok sorry for the delay, I faced the same problem on my brother's laptop this week end. I was stuck with this black screen and the game would only work in windowed mode (with flashing lights all along).
The solution is indeed really simple:
1-Install your latest video drivers
(check
http://www.my-config.com if you are not sure)
2-Install the latest version of DirectX
(see Microsoft website for "DirectX End-User Runtimes (June 2008)")
3-Restart your computer
Then it should work fine
Tell me if you still have troubles...