Next step is to get your scope working, and get an image on it. This will let you probe the video section, to try to narrow things down.
Unplug the monitor for now, and leave it that way until further notice.
Put the scope in XY mode, put the probes on the XOUT and YOUT test points of the game board. Also, one of the probes will need its ground connection connected to any GND test point on the main board. Adjust the X and Y vertical settings until you can get an image on the scope that generally resembles what you see on the scope screen. If you need help with the scope, there are probably tutorials on youtube that can help you.
We could keep guessing here, but more data will make things easier. My guess is either one of the new chips you put in the video section is bad, or potentially there's a broken trace somewhere in the video section, possibly under one of the chips you socketed, or from someone else's past work.
But once you get your scope set up in XY mode on the XOUT/YOUT test points, we can give further instructions.