If it just plain stops (and the pounding in your head with it) almost surely the sap pump. My wife's has a bad bearing and it's a horrible howl.

I have foxwell scanner it can engage the pump to know for sure but you can confirm by putting your hand on the pump while you have somebody else start the car.

SAP on e53 M54 is painfully easy to find It's directly behind the right headlight and the filter for It is the most obvious thing above the right wheel well. Follow the intake hose from the filter to the air pump. It will be obvious.

__________________
2011 E70 • N55 (me)
2012 E70 • N63 (wife)