Retrofit cnc 3axis

If I want to restore it, I can always do it as long as I reassemble the card, the original PC and connect the right cable?

Yes (at least if our analysis is correct) The idea is to disconnect the two flat ribbon cables on the processor board:
 
Then you can remove the pc-motherboard, the processor board and the interconnection board (the one with all the large black connectors). The easiest would be to buy terminal boards for each of the two ribbon connectors  (like the ones you got for the db25 but with different connectors) and wire the signals from there to the new breakout board.
Before you do that you would want to find out as much as you can about the pin out of those two ribbon connectors with your DVM.

Not a DB25 most probably, but some other connector with 25 pins.

Yes something like this but with the correct number of pins of course
www.aliexpress.com/item/32799636212.html

Before that to perform the tests on the pins of the flat cables with the DVM do I have to disconnect them from the processor board (white)?

You may have to apply a mixed strategy like before on the db25 connector. You can try continuity testing with the power off and voltage measurement with the machine running to find what is happening when different functions are activated. First thing you will want to figure out with the machine off is to find a ground connection to clamp your voltage meter to before you start to measure voltages. I would expect that some pins on those connectors could be traced directly to the drives but if the pins on the drives connectors are not labeled then that might be of limited use.

And do I already have the IDC adapters for my cables?

I don't know, I have not seen any.

Probing on these connectors can be a bit tricky but the pins will be connected to parts on the pcb board that can be found by continuity testing. That would be my approach to find the pinout.
The fact that you have probably 16 outputs and likely just as many inputs make it easier to identify one part on the board that is directly connected to the connector and use that knowledge to find all the other outputs and inputs on the board.

As tommylight has already suggested, one of the three pins of the transistors is likely connected directly to a pin of the output connector.

The transistors are the little black parts that you see in four groups of four above the connector. Looking at the image of the pcb I would guess it's the the top pins that point away from the connector.

For the input side we would need a better image with the flat ribbon cable removed to reveal what is underneath.