Have you done all the usual checks? Compatible lamps? Properly connected? All wires reattached? Lighting Fuses? Any warnings on the check control?

What happens if you put the old lamps back in? I know one is blown, but at least you can get back to a known status and then only make one change at a time and work forward. If they don't work then you'll need to have a means of checking supply

Have you a way of checking volts on the pins at the input side of the starter ballasts, or normal DRL and non-HID bulbs. If there's no 12V supply then look at the fuses. DON'T check voltages at the HID connections on the lamps themselves as this could be of the order of 25,000 Volts for a few seconds before dropping down, but those few moments can cause serious injury or death!!

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Me:
Current: 2011 E71 40D Vermilion Red/Beige Nappa

Wifey:
Current: 2012 R80 Countryman SDX Green/Cream