Let many other people already said, try the 2nd key first, and get back to us. If the coil in the key goes bad, the ignition switch won't send signal to starter motor, because the system is thinking the key is a cut-out duplicate, not with the chip.

If the starter is good, it's either key or ignition switch. Otherwise, it should at least crank. Oh wait, what if the crankshaft (NOT camshaft) positioning sensor goes bad in the cold temperature? Can you hook up a OBDII reader and check if there's any code throwing up?

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01' 3.0i E53 (M54) with 164,000 miles
07' 3.0si E83 (N52) with 134,000 miles
08' 3.0si E70 (N52) with 91,000 miles