When in the NGX and I push the activation key, I hear a click and the mouse pointer turns into a hand, but no activation screen appears. All other a/c are okay.
That's not a GSX problem, of course. It's likely that you have assigned one of the PMDG cockpit functions to the same hotkey as in GSX so, the PMDG one is taking the precedence, because from your description, it looks like a cockpit function is being activated. By default, no PMDG key conflict with GSX so, it's surely something you customized in it.
Or, it's the opposite: you changed the default GSX hotkey (CTRL+F12) and chose something that was already assigned to the PMDG cockpit.
You can choose what to change, either use the "Change key assignment" in the Couatl menu to change the GSX hotkey to something else, or use the similar function in the PMDG menu to change it there.