I just probed the address and data lines of the CPU and there's definitely activity. What should I try next?
That's a good sign. I'm guessing the RAM boards are ok as they worked before, right? You could also try with just one CPU board or the other if you happen to have two.
Without RAM, there's nothing that can be displayed.
I'd look at the CPU board schematics and locate the VSROM and the things it talks to - that's the video state machine. Something around there's not working - though it could be something related to the analog board. I do see some diagonal lines on the display, those are a sign that some horizontal retrace is happening.
I take it you've played around with the trimpots on the video board using a plastic screwdriver already.
Some other things to try, pin #19 (CB2) on VIA #1 (with the other end to GND) produces sound via a timer + shift register output so I'd attach the scope to that and power it on, it might be trying to beep some codes but if the speaker isn't working you won't hear them. The scope should be able to pick up the tones graphically and you could figure out what they're trying to say:
https://lisafaq.sunder.net/single.html#lisafaq-hw-rom_beeps - you might have trouble telling high vs low tones apart graphically if they're all high or all low, so you might need to guess around those codes. Might help if the scope has some audible mode to help you with that, or if you have something you could attach to that pin that leads to an amplifier - but be careful not to fry your VIA. An old pen style logic probe that beeps might do the trick to get sound out also.
If you see nothing, either the CPU can't talk to the VIA or something else is broken along the path from the CPU board to the I/O board.
If you have a spare VSROM to swap out that would help eliminate that. If not you might try this one:
https://www.ebay.com/itm/142796459701 - but it could also be something else around there.
Inserting a blank or PC formatted floppy might be useful too though it might also eat it and not let go until you fix the problem - the idea here is that it will see the floppy as unreadable and should eject it. That would tell you that the 68000 and the Boot ROM are working.
Another thought which you might be able to verify if you don't detect any beeps: Since you're not seeing video, and you're not hearing beeps or clicks or anything like that, it might also be the motherboard. Perhaps some contacts aren't touching or are dirty and so the CPU board video state machine can't read the RAM and turn it into a video signal and it can't talk to the I/O board so it can't beep.
Checking for broken solder joints on the motherboard where the CPU connector is might help, as would cleaning the contacts, reflowing the solder, etc.
