I will revert back once I change PSU if anyone is interested.
I am interested, please update.
Changing PSU did not help. A single board that sometimes had 0 chips instantly started hashing, while other two were not hashing like on old PSU but after a single restart it disappeared as well. 0 out of 65 chips read on all boards.
PSU that I put in now was new (ordered from Bitmain) and was tested on working unit, which means that it is not a problem.
Control board cannot be the problem as I have tested it on working unit as well. Data cables I am yet to test but I doubt they are the problem.
I will quote this message in
THIS THREAD as that is where it might help people. I will provide pictures of a single hashboard which I think started the chain reaction of all boards going down.
Here are three photos of hashboard that first started making problems:
https://imgur.com/a/ZhxhMsOHere is why I think this board is the reason my old PSU and other two hashboards are dead as well:

Discoloration on one of chips (in middle of picture) means that it probably burnt. How or why I am not sure. What that one does I am also not sure. It's name is "copper_26". I'd appreciate if someone more tech-savy with Antminers could tell us what that chip is used for and why might it have burned?
I am usually used to seeing heatsinks shorting hashboards or falling off, but I've never seen this chip get burned.