OK well first things first. Do you know how to interpret a video signal on the scope?
Triggering might be a bit tricky, but you should see something like this on the scope:
I'm going from memory as it's a loooong time since I worked on video, but the above represents a horizontal line and should be at 15kHz-ish. The levels at the front/back porch should be ~0v which represents black or rather no colour for that channel. The negative going pulses are the sync and the waveform in between is the actual video. 0v=dark 700mV=max. (forget the color burst, that's for composite not RGB)
The 4066s will be for switching the video between sources so check them, and the digital switching signals on pins 5,6,12,13. One of the 4066 switches may also switch the video signal to 0v during the front or back porch, this is to ensure that "dark" is actually 0v and is what I was referring to earlier by DC clamping.
At least you have working boards to compare against which should make life a bit simpler!
What you show is a composite video signal, that won't be the case here because this is RGB. I've only worked on the monitors used in these systems because they're also used in arcade game cabinets but they use analog RGB that is typically 4V full on, 1V black, 0.8V blank and then TTL level sync which can be separate H-V or composite sync.
Look at the pins on each side of one of the switch elements in a 4066 and compare to the same points on a working board. Do this test in-system.