Thanks in advance for your advices.

I installed, Ubuntu 12.04 today, on my PC with a Radeon hd5670 graphics card. The first error I encountered, (just like the first time Unity came out - after witch I waited to try Ubuntu again until now) is, that it hanged after login at the desktop wallpaper, with only the mouse cursor. Well actually the first problem was with the live CD, but I managed to install it, using the install now, not the try now. Live CD has the same problem, as after install.
So, after installing and getting the error, I searched of course before asking this
I found this: http://askubuntu.com/questions/12009...-purple-screen

The accepted answer there helped me to get to this. (note, that the below picture is a screen taken from a working desktop, and then erased the parts that don't show on mine.)

Note that there is nothing at the top except the brown bar. No shutdown button, no nothing. The system hangs, I can't click on anything, I can only wiggle around with my mouse XD