The "beat" pattern you see is typical when you don't have the sampling phase and rate perfectly adjusted. All analog to digital video convertors (including the one in LCD panels) have this problem. Most have an "auto" button to set this, but many rely on standardized VESA modes to look up the optimal settings. The Mac's default checkerboard background is actually the best thing to have on screen when adjusting for the correct timings. You'll know when you get it right because the background becomes pixel perfect. The Acorn likely uses TV-RGB (240p or 252p for 50Hz modes)....those take trial and error since there wasn't one "standard" for horizontal pixel clocks on them.
I’m really doubting the drives are dead. Obviously there is a LOT of something built up on the disk, even if you can’t see it.
Cleaning diskettes are a lot more abrasive than a cotton swab, so it would be nice if you had a single-side cleaning disk.
One thing you could probably try is, with the drive open, hold the spring-loaded pressure pad up with your finger and insert a standard cleaning diskette with some alcohol on it. This way you won’t rip the felt pad off from it getting caught on the cleaning disk.
I’m betting it’s a thick layer of grime. Had it happen on old PCs many times. Insert an unknown disk and all of the sudden it won’t read anything.
Update: I finally had success by switching the solder tip from a blunt chisel to a pointed tip. I held the tip perpendicular to the board and pushed it into the hole on the bottom side and had my solder sucker ready on the other. At first it seemed pointless because the tip was obviously not going to get hot enough to melt the solder, but after turning my iron to around 700F it suddenly melted and pushed through all that old solder. This is the first time I was actually able to get the solder sucker to work!
Thanks for everyone’s help! Now I just need to test all the connections, then clean it up and put it all back together to see if I’ve got sound!
I cleaned the ROM chips and I already resoldered J4 pins on the analog board some time ago, but I got these results: I still got the same checkerboard screen, but the speaker did a little “thud” sound when it switched from checkerboard to the gray screen and the speaker screeched a bit when the diskette icon appeared. I have very little experience with electronics but this makes me think that certain parts of the circuit are not getting enough voltage to operate which results into checkerboard and silent speaker.