THANK YOU! To all the people who help me during this repair, expecially @xavier60.
The guilty is the 1N823, thermally compensated zener diode. (
https://4donline.ihs.com/images/VipMasterIC/IC/AMPD/AMPDS00002/AMPDS00002-1.pdf?hkey=6D3A4C79FDBF58556ACFDE234799DDF0)
I've put a 1N4735A (6.2V zener), I get now 12.35V and 5.3V almost with the actual load. (A pretty old pata 40Gb HDD).
Find attached a few picture. (I may have to replace the blue cap - should be 1n5K400 from another picture I have - that I've accidentally melt a bit).
Now I have to find a seller with decent shipping price. This diode is 4Eur almost and 20Eur shipping :-(
I must admit that the 1N4735 that I've mounted works well, even if I heat up with the heat gun it goes up to 5.35V and 12.45V, which I think could be in the IBM 5160 motherboard limits.
Now I'm going to reassembly that PSU and check it connected with the PC.
What's your opinion about leaving the 1n4735 there?