Since my camera has the infamous small cracking on the LCD, I'm sending my camera to the Olympus service to change the LCD and to test the mode dial too.
I think you are correct, perhaps my camera is the problem and not the Nauticam housing!
Thanks, I'll post here the outcome of this strange problem.
Just to let you know that Olympus has repaired successfully my OMD and now, the camera works properly inside the fantastic Nauticam housing. They replaced the cracked LCD, glued properly the mode dial and fixed the internal problem and everything is ok now.
Thank you all for your help!!