I've found a firmware for my monitor (exect model). Yes, those are real i2c eproms.
Also I decided just in case to solder my external 5 V and 12 V power supplies omitting built-in one. I desoldered transformer. Also I discovered a blob dripped (most likely) from the transformer. See attachments, the blob is located under the transformer, indicating that gravity pulled down that substance from the transformer.
After soldering 12 V and 5 V power supplies, the monitor worked perfectly.
It is still a mistery on why it did work with dvi-d connected to a PC and not with VGA.
If anybody can explain this, I'd be eternally thankful.
As for the monitor's PSU. Is the transormer a culprit of this? My explanation on why 12 V line was 14 V is that 5 V coil's isolative coating melted and it created a short, effectively reducing number of windings. That led to drop in voltage on 5 V line. Since optocoupler is connected to 5 V isolated line, it fedback into IC, which stabilized 5 V line, but also increase 12 V line. Is this explanation plausible?
As for repair, firstly I want to get what a real culprit is. If it is the transformer, I'll just remove that part of a PCB and insert PCB from 12 V PSU and buckconverter to 5 V. Monitor takes 1.3 A @ 12V and 1.3 A @ 5V. Therefore 3A@12V is sufficient.