Here is a video of the problem. No buzzing from the electric fuel pump when engaging the ignition. Cranking works fine but engine is totally dried out:

BMW X5 E53 Cold start problem - no start - YouTube

In this second video I have tried starting MANY times (appr. 30) and now sudddenly the electric feeder pump kicks in every time I turn on the ignition. You can hear it buzzing in the background. Engine starts with ease. Today heating the engine compartment seemed to have little or no effect for some reason:

BMW X5 E53 Cold start problem - starting - YouTube

I talked to the dealer today and I´m taking the car back in a week. This time I will let it sit there until the problem is solved. I also sent them these videos.