The radio of my 2014 Silverado stopped working. When there is little daylight and I turn on the ignition I can see the monitor glows a bit but no picture will come up. So there is power available, I also checked the fuses.
Which part must be checked and maybe needs to be replaced? Could it be the „Communication Module Box“? Is the radio a part of it?

 

If it's getting power then it's probably just dead. Stereos aren't really user serviceable.

 

I don't expect it to be serviceable, but I'd like to know if replacing the „Communication Module Box“ could be a good idea.

 

The "Communication Module Box" is probably your Telematics Communication Interface Control Module (TCICM), and it's responsible for the old 2G Onstar service, which is no longer operational anyway.
They'll sell you an updated one for around $1k , but I don't think it'll revive your stereo display. Does sound come out?

 

It's not only the display, There's no sound at all. I cannot even eject the CD I was listening to.