Hi Sam,
Thanks the PRAM reset worked - hooray! I've been on meetings all day today so good job it did!
However tonight I wanted to start up my own trusty MBP (one year older than the university laptop ...2011) for a personal Zoom meeting today and I am seriously worried. I press 'Start', hear the familiar chime and some whirring, see a white screen briefly and then it goes black. I tried the methods you suggested for the other laptop but neither of them change anything. Doing a Pram reset (and holding the keys down) it chimed, whirred and went from white screen to black continuously till I took my fingers off.
WAIT - I've just opened the laptop and the screen is there!!! I don't know what on earth happened! Anyway it looks like all might be well after all so false alarm. I just wish I knew what I did to help it in case it happens again!
Thanks again Sam,
Tilly