I just found the fix for this and I wasn't sure if it had already been posted so I thought I'd add it here and in the TFN Frequently Asked Questions post.
Question 9. When I start the game, the opening videos are blank yet I can still hear it. This worked fine on Windows XP but is broken for Windows 7.
Answer: Right click on your Vampire - Bloodlines desktop icon and open properties. Click on the "compatibility" tab and check mark "Disable Visual Themes" and "Disable Desktop Composition".