Don't know if you've tried this but, engine off, chock two wheels, jack up another wheel, (just one), make sure the transfer box is in H or L and the main box is in any gear, (but say 4th gear), have someone rotate the jacked up wheel whilst you crawl beneath the vehicle and see if you can hear any noises that may point to where the drive is broken.
I don't know, but it may be that some input shafts may break or clutch centres fail, maybe the centre diff has failed, listening around under the vehicle may give a location.
My old Range Rover classic snapped the front diff pinion shaft off inside the diff housing so you could see nothing from outside but all drive was lost. Only drivable by engaging the centre diff lock, which you apparently don't have.

This page https://www.ashcroft-transmissions.co.uk/miscellaneous/disco-ii-difflock/disco-ii-diff-lock.html
gives you the serial numbers on the Transfer boxes on disco 2s. Some had the internals but no connection to the HiLo lever, and some didn't even have the internals in the box.
So if the number begins with 41D, 42D or 68D, you DO have the necessary to lock the diff, you just cannot do it from the lever. I fear your's is too recent. By then it was an option so you either had it or you didn't and the plate on the upright of the console tells you if you have it or not.

Is there any noticeable difference in resistance between gears when you push the vehicle ? Try different gears on both the main gearbox and the t-box.