In Windows Explorer, you can browse to the '..\Beyond Divinity\Static' folder to view the 'intro.mpg' video. Rename that file and the game will skip playing it on startup. That may not help (it did in a couple cases of a crash after the video: see here), but it will at least remove a step each time you try the game.

Someone had a problem with the game automatically minimizing during the intro movie and crashing if they tried to maximize it (BattleFields N00b ?), which was fixed by a Windows patch for XP. Another person recently had a similar issue in Windows 7 when they tried Win9x compatibility mode, which was fixed by changing the desktop colour depth from 32bit to 16bit.

A few people with problems on startup could avoid it by setting their desktop resolution and the game resolution to be the same. You could also just try a lower resolution, to see if that helps.

Are you shutting down all non-essential programs (especially anti-virus) before starting the game?

There may be some things you have not tried yet in the topic below, as well.

yet another "Game simply won't start!"-thread