Another approach if the already mentioned solutions do not help is to start the mod by double clicking one of the scenarios in the Public Maps folder. If the game "crashes" again for no apparent reason, open your task manager and see if there is still a Civ4BeyondSword process running. If so, wait a moment (you can try to increase its priority). The mod needs some time to start on some machines, especially if you're running it for the first time.