Finnaly got the time to fix it.
The read problem was fixed by resoldering the LA chip (and the components around it)
Now the PS2 reads CD/DVD/PSX/PS2 games perfectly.
But I got a KHS-400C in a v3 (it had a KHS-400B originally) , which works fine, but I would bend/destroy the cable to the laser, when the laser tries to read at the outer edge of the disc.
I had some broken lasers, so I tried to bend, very gentle the connector on the laser, to 40-45 degrees angle, It looked like it would work. So I did this trick to my new laser... And it worked perfecly, checked that the cable didn't bend while reading the outer edge.
But be carefull if you would try this trick, because when I tried bending it to an 45-50 degrees angle, it just came off (did it on the broken laser, not the working one!).
Thanks for all the help, now I gonna go and play some games!