When the BST connection blows it forces the cable back. If you push the cable toward the battery and pay close attention you can feel it move a bit. However, even if the cable has be fired back the engine should still start but not have enough voltage to support systems such as airbag. Make sure the new ignition switch is the correct part number for your vehicle and their isn't a problem stemming from the install. I have seen exactly your problem and it was caused by the ignition switch. And, recall that everything was fine for 3 weeks after you installed the new switch and symptoms are now the same as the old switch.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas