Following a combination of recent flat battery and water ingress from that
quarter window the DSP and Mk3 nav is now not showing up in the console.
Light around radio knob goes on and radio shows up in that emergency blue color
display that replaces the Mk3 one. I tried swapping in a MkIV nav, its screen comes up nicely
but the head unit also does not list the DSP in that case.

Following the water incident the sound and DSP has come on intermittently now and then.
But last week after a recent flat battery incident they disappeared from the head unit.
No sound, Mk3 nav shows no screen, becomes replaced by some bluish default UI probably provided by the head unit.
Could it be the Mk3 nav has lost its firmware ? Is there a CD out there that
allow reflasing it ? I hear some seeks on the CD initially after insertion, then no more activity and the red LED on the drive keeps on flashing. I have made sure the CD is clean and it seems readable in a regular PC.

I might even be willing to swap my MkIV for a fully working and genuine RR Mk3 nav if you have one.
I cherish that fine british female voice of the original map CD, "you have arrived", "if possible make a U turn", etc.
My Mk IV runs firmware V32 and has a Range Rover logo displayed. It comes with some U.K map disc
that is plain useless in Sweden but a UK owner would likely be pleased.

I will check fuses as well. The radio unit sits very crammed beside the
wheel bay, is there a recommended way of getting better access to it for examining its harness ?

Thanks for any advice from you who went before me.

Try removing the amp and nav computer and putting in the airing cupboard for a few days. Then clean all contacts with contact cleaner and refit. Might be enough to get them working. Where are you? Someone local might be able to help with working components as a trial.

I´m in Sweden. I took a look now at the DSP connectors and it seems the ground pin #15 of the main (heavy gauge wire) DSP connector is broken off due to corrosion. That pin now sits firmly in the harness connector pin 15 female socket.
So I will need to get the DSP apart and solder a new ground cable arrangement. Seems other have experienced this fault.
This may explain why the DSP sometimes lost audio when using flashers or brake light turning on (ground fault).

And the Mk3 nav seems to be bricked. Manuals say it can be destroyed if battery power is lost before a certain period of time after ignition off ? I recently had a flat battery and some voltage dropping starting attempts that could have had this happen. It has had its share of water ingress as well. I will pick one up on Ebay. I have a MkIV as well that will suffice to test out the DSP once I eventually succeed in reviving it.

The radio unit seems to work since it shows its station tuning on screen despite the loss of audio. The expired analog TV unit works as well. Later on I will look at finding one of those BMW terrestrial digital TV hybrid tuners to replace it.
I seem to understand that tuner work only with the MkIV nav.