You need to be moving around 5 mph with trans in Neutral or try Neutral, Drive then Neutral to select Low (forward), it's just the nature of a gear to gear box, it's bound up and needs to unspool through the transmission. Only Lock it when on dirt, gravel or snow or testing on pavement while traveling in a straight line for a short distance. When the transfer case is Locked there should be light on the dash.

 

 

 

That doesn't look right it seems that you have 3 positions side to side it should only be 2 left is lock and right is unlocked then you should also have 3 positions forward to rear that would be low at the furthest forward position neutral center and high towards the back. You will need to look closely at the linkage.

 

I have looked at the linkage from underneath and everything is connected. I had someone move the shifter left and right and I can see the selector moving to two positions but when he tries to move forward there is nothing the other lever does not move. I can see a very slight movement. Hard to tell if anything is bent from under the car. Definitely a tight space. I guess next step is to try rolling as mentioned above and take out the center console and see what is going on.

My only thought on 3 positions is that it is in some type of bind and the middle position is where it rests with no pressure applied.

I find it odd that it moves left to right as in the video at all times.

 

If you put the shifter in neutral while the engine is running then shift the transfer case lever to the middle from the left to right motion then shift the shifter to D will it move forward or just rev when you press the accelerator?

 

It will move forward. I can not move the shifter to any spot where it just revs.

I will try again this afternoon when I get home and see if I can get it to move while in neutral at 5 mph.

 

it does appear to have 3 positions side to side as noted by Icannap1

(dam pic wont upload) Refer to Allbrit parts diagram
Allbrit MG ROVER & Land Rover Ersatzteilkatalog
transfer box - LT230 - gear change manual

for the following:
I had bolt no. 5 (see pic) come loose a while back while wheeling and think this may be 1 part of the issue (and causing the 3 positions). So instead of rod 13 piviting rod 18 - rod 13 just slides over.
the other may be seized linkage for the low range
I had to remove the console and drill out the F-ing rivits of the boot to get to the top of the case. The console can be tricky and is likely brittle now so be patient - It will be a combo of moving the auto shifter and ebrake till you find the way it wants to come out IIRC.