Thanks for the responses and ideas.
We can't tell how much of the LA is working, because the display doesn't show anything useful. It is believed to have been operating before being stored, so there's good reason to hope it can be resurrected.
The only change we can see is that after maybe a minute the "semi-solid rectanglar blocks" change appearance slightly, but only once. That tends to mean something different is trying to be displayed, but there's insufficient information as to whether or not that is because the processor/program is functioning correctly.
The built-in extender card is very nice; I had noticed the socket and wondered what it was!
As for "learning opportunity", we have plenty of them, and some of us are quite adept at resurrecting 70s/80s scopes and plotters

Personally I can't be bothered with scopes (other than my HP1740), but since we don't have an LA I'm prepared to put some time in.