The screen ONLY opens up when the ignition is turned on. Normally, on E46's, X5's etc with the 'always visible' screen, then the splash can be seen when the car is unlocked and the door opened.

In the X3, at this point, the screen is closed and hidden from view and the splash has usually 'timed out' by the time the ignition is on and the screen has opened up.

You could try this - after switching off the ignition, manually pop the screen open (you can do this without causing any damage). Lock the car , wait 30 mins or so, go back and unlock the car and open the door. See if the splash displays then... I have a feeling though that the screen may 'recycle' and close then open, but as I've never tried it, I can't be sure.

I look on it as whilst the splash screen CAN be a cool thing to impress the girlies, so can the screen popping up out of the dash....