That's a weird one... differences between two modes would be how it gets power, direct 5v in PS/2 mode, and by a charge pump in serial mode I think. Then the PS/2 connection is at higher rate than serial I believe so some capacitor gone out of spec could maybe allow one and not other.

if you have a scope you can look at the difference between two ps2 mice https://www.youtube.com/watch?v=7aXbh9VUB3U

Later in the afternoon I will open the mouse to check if I do have +5v on the chip. I can see there are some diodes on the pcb in the cir unit of the mouse and I would like to ask if these get damaged or not. It Is my first mouse bought on 1996.

Back to the saga. I measured the +5v from the socket to the most a 5,05v and just after the diode the voltage drops to 4.8 v. This is the only diode that drops the vcc of the vdd pin 5 that much. Do you think the diode is to blame?The same scenario with the serial adaptor outputs 5,8v before the diode and 5,3v after the diode up to the vdd of ic controller. I am now soldering a bypass to the diode to check the ps2 functionality.

Here I post the same measurements but in serial mode which is working okey. The ic as per the datasheet works with vdd rande of 4,0 v to 6,0v. Can I actually bypass the diode without harming the components?

Well you can try for a test on PS/2 I guess, but don't plug it into serial like that, have a feeling it's protecting the power pin from seeing -12V or other transients from serial. The spec of the chip saying 4-6V probably means it works down to 3.5V even but flaky under some circumstances so I don't think the typical diode voltage drop is affecting it much when it's still a bit over 4V

The saga reaches an end successfully. I made a simple bridge and the mouse works first time after 25 years in ps2 mode. The vdd is not 5,0v on the ic. Now I would like to ask what have happened and the diode deteriorated. Is it because of hot plugging a ps2 maybe?

Possibly, or static electricity damage, I would replace it with a low power schottky diode to try to keep everything in spec for both modes.

Yew of course I will replace the bridge to a diode. At this age we forget easily and I will use it again on my micronics w6li again in serial mode. Thank you.