My 1st gear switch connector hadn’t been fully pushed home, probably because of a small piece of grit. Cleaned it all and like you, voila! HDC works perfectly.
Just to finish this off, the battery-disconnect-reset worked OK, And the radio was fine (no code needed), but after a week and a short drive with the rear window open, the cab switch for the rear window went awol again. I repeated the reset which...
@Kerlaan
Once I'd worked out where the switch was, I found nothing connected to it. There was a connector tucked neatly out of the way behind some fittings on the body nearby that fitted, so I tried it out and the system works perfectly now...
I had similar when I first had my freelander. I asked a BMW specialist to do the leak-off test (it's a standard procedure and they told me how much it would cost to run the test) which came back with one of the injectors way out of spec and...
While not necessarily directly related, changing the gearbox oil in mine made a noticeable difference to the smoothness of shifting. If it hasn't been done for a long time, it's worth doing.
Thanks for following this up! I'll give it a go sometime...... Tell me, did you have to put a security code into your CD player afterwards? I think if so, I will have to get a new one as I don't have any documentation with mine.