I had exactly the same problem (black boxes, missing graphics).
I did the following:
- I carefully updated all the video drivers (both using Windows Update and the graphics manufacturers website)
- Updated DirectX to the latest version (from the microsoft site)
But what really seemed to work is dropping the Graphics quality (From Wallace+Gromit Settings menu). Dropping it for 4 to 3 seemed to immediately solve all my problems (maybe not enough video ram?). Try seeing if dropping the graphics quality helps for you at all.