You should search the archives on "xenon ballast" another name for the igniter. I know one of us has either tried this or succeeded at bypassing the dead one with a new one. From what I remember, xenon lighting is a unit, not a sum of individual parts as on some other brands.
If you don't find what you need here, e46fanatics or bimmerforums may be other resources to try. Use google's site: command for better results.