Work through the troubleshooting section in the service manual:
https://siglentna.com/download/6149/
Thank you for the link tautech, the copy I found while googling lacked the diagrams and useful sections at the end.
The rails all seem to meet the ripple spec, if marginally. Miraculously the scope began booting again the other day, sometimes rapidly displaying the original issue and sometimes remaining perfectly stable. Enough so that I was able to run a firmware upgrade and self cal. It doesn't seem to have improved the situation at all and it still regularly locks up at boot for a dozen or so attempts.
It can be accessed from the network, does that still work?
Unfortunately no, it stops responding to pings and fails to load the web interface once the display disruption begins.
Interestingly the screen recovers over time and the white lines disappear. The scope continues to correctly display live waveforms although the buttons, knobs and network remain down. Any ongoing data collection, statistics or onscreen measurements freeze however.