I just wanted to leave a note here in case it helps anyone in the future searching for a fix. The other day my 54645A scope failed to power-up, without any warning. It seemed to be a PSU fault.
Via a lucky stroke I came across an 11 year old post on an Agilent forum saying the poster had found resistor R27, 330K/~600mW had gone high and replacing it fixed the PSU.
Sure enough, that was the exact same fault and fix for me !
I think it's possible the same PSU may have been used in other 54600 series models, so I'll list them here for search purposes:
54600B
54645A
54645D
54602B
54610B
54615B
54616B
54616C