Do you have another camera to try the shutter release on.
Just plugged mine in to see what it did. Only way rear screen came on was if I pressed the live view button.
I read some instances where the rear screen didn't work when plugged in due to a short in the release cable.
Other than a bad shutter release cable or an accidental press of live view, I don't know what's happening there.
Oops thought this was about the D500 that's in your camera list, just noticed this is in the D750 section.