Artur,
Unfortunately my program at work is not working right now. Without the wiring diagrams in front of me, I'd be guessing at best. If you can wait until Monday, I'll see what I can find out then.
Working from memory, I think I would look at a couple of things. First, the best way to troubleshoot it would be to have a dealership or service station connect an NGS test stand (that's what they're called here in teh states, but I don't know if anyone uses them in Poland). From there, they could view the GEM PIDs (inputs and outputs) to see exactly WHY the 4 wheel drive is being called for. It could be a wheel speed sensor or shaft speed sensor that's not working correctly, making the GEM think that the wheels are slipping when they are not. In that case, it would be a simple sensor problem, not something more complex.
The other possibility is that the system is not calling for the 4wd to engage, but some other electrical problem is sending a false signal to the Torque On Demand relay or the brown wire. Again, without the schematics, I can't begin to tell you where to focus right now.
Sorry I can't be more specific for you....
-Joe