Do you have an XY monitor? There is video out connectors on the rear of the unit which you can use to obtain video. You can also probe those with an oscilloscope to check for a video waveform if nothing else. Iirc the rear XY signal is a separate signal chain from the main signal driving the display.
I have the 3585B and I use it very frequently. It’s a very good SA for doing work below 40m. I’ve had to do two repairs to mine so far. The display board, A67 I believe, had shorted tants on one of the power rails, the -15v I believe. That was an “easy” fix. The second repair occurred when the flyback transformer suffered a short on the secondary side. That one was a bit more painful as it required a bit of cash for replacement parts. Although that failure was not terminal as, like I mentioned, I had video from the rear ports making it somewhat usable albeit without the graticule. The manual has very good troubleshooting guides. I’d recommend getting familiar with it.
