I do have an oscilloscope and a logic analyzer. Originally the flip flop triggering the ROM chip select was stuck between levels so I replaced it. I haven't checked the capacitors but the power levels are all good.

Strangely, sometimes when I turn it on I get a different behavior. The screen rolls no matter how I adjust the brightness and contrast. When I press the reset buttons, the checkerboard turns purple and then is replaced by vertical lines. The buzzing does not stop and the "rus" LED does not turn off. This happens randomly, I can't find any pattern. I think my next step should be to replace all the capacitors.

I don't know how to upload a video here but here are two screenshots of what happens.