Thank you, Eric!
I eventually unscrewed that ring, although it wasn't as simple as gripping it and turning it counterclockwise.
With regards to the battery, I am evaluating the options, as I am reluctant to install any NiCd / NiMH batteries which might leak at some point.
I eventually mustered the courage and opened the big & heavy box and, funnily enough, checking the electrolytic caps in there, almost all of them had less than half their rated capacity, although their ESR was ok.

I replaced the caps and re-assembled the box.
On to the display unit now...