I have a similar problem but with ubuntu 10.04 and wine 1.2. Someone replied to this post to say that he should update wine, but my wine is the latest version.
Basically, I try to run Diablo 2 and the two Blizzard opening videos run fine, but the main menu won't load. There's just a black screen with a hint of the ubuntu tool bars around and I can only hit esc to close everything and go back to the ubuntu desktop.
I've run the video test and it suggested the 3d mode. I've tried both the 3d and 2d video and both have the same result.
Any help would be greatly appreciated.