Anyway, there has been an interesting development. My "analysis" wasn't actually that different, I saw two pins going to the same place on the PCB so I was thinking "OK, whatever is coming out of those two pins, it must be in pair because one pin is perhaps not enough". So I did it, I desoldered the transformer, to check what's wrong.
When you look at the transformer, you would immediatelly think something like "Oh suuure, it is the broken pin on the right", right?
Wrong. The pin on the right is the unused pin, there is no hole for it on the PCB. So yes, it is the left one which got loose. Strange, huh?
So I was looking at that hole *in plastic* seeing absolutely no sign of anything conductible whatsoever (there is only one other pin with "setup" like that, others have something coming out of the transformer). I was like YOLO, let's take the loose pin, warm it up and just smash it into the plastic, hoping that there is *something* conductible inside, some magical pudding
Did it work? Hell yes it did! Well, maybe. I let the TT run without PSU cover for about two hours - I have recapped the whole MegaSTE PSU while running YAARTTT (yup, had zero faith that it would work so I was preparing this PSU for the TT), Storm, Thunder, IDE SD card reader installed. I still have to try it with the Lighting + Mach64. But it's a good sign. It's true that maybe it is a coincidence - remember I did resolder all the joints, I even fixed some joints which looked suspicious (while comparing it to the other PSU), so who knows.
I'll report when I will have it all up and running.