Mac Classic: not well know ... chessboard problem

One of my Classic Macs has strange problems with display and of course booting up. It seems to be similar to well known on-motherboard-capacitors problem (e.g. https://www.youtube.com/watch?v=5GivbpvLpm4) but the issue is that on other system the motherboard works well without chessboard on screen. Also - other motherboard on the Classic in question doesn't resolve the problem. I see the same on the screen - a little bit floating chessboard:



If you prefer movie it is available here: http://www.tomekrys.pl/tmp/mac_szachownica_film.MOV

Any ideas?

Do you suggest to replace all capacitors on analog board?