It might not be the BCM at fault, if I were you I would find a local BMW independant garage in your area, and ask them if they have anyone in the shop who knows about BMW's from 2000 to 2005, specifically the X5 (which a lot of electronics were also in your Range Rover L322 of the time )
https://en.wikipedia.org/wiki/BMW_M62 - specifically M62TUB44 engines in the E38, E39 and E53 BMW cars/models that all had the same key programming and electronics !
If they do have someone, ask them if they can access your EWS ( this is under the gear lever console in the middle of the car) , see 14 seconds into this youtube video
some shops use a AK90
Your local shop will trust something that they are used to for the BMW's they service, they will be able to program a second key for you, I just got a new one for my 2004 car, a flip style one, and I watched them do it, took 40 minutes from start to finish
At the same time they may be able to scan your car, and look into what maybe at fault with your BCM, did the dealer tell you the error codes or the ODBII codes that came up when they scanned your car ?
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