After having spent a considerable part of the Christmas trying to install the
GPIO library I finally just found the answer. As I have noticed there are numerous others with the same problem, "no module with this name", so I thought I'd write a little notice about it. There seems to be as many ideas how to deal with this problem as there are answerers. But no one except for the last one could see the real problem. Look at this line:
import RPI.GPIO as GPIO. It won't work. Do you know why?
Because the I in RPI shall not be capital but small case, RPi.
A dirty trick if you ask me. I wonder how many that are struggling with this right now. You must also be superuser to make it work, open idle like this: sudo idle,will do it.
Another thing that I found a little strange was this. Before different suggestions on how to this and that, there was often a text in big letters:
CODE:SELECT ALL. Was I supposed to write that or what is it?