I closed the thread "blurred text" with all the deep and helpful stuff.
I have some new information that I like to share with you now.
The resolution problem was solved after I used the DVI input on my monitor. After swapping the cards the nVIDIA also worked fine when the monitor was connected to the DVI output.
So my complaints about nVIDIA were not really fair. Sorry 'bout that!
I sold the ATi card that I had bought because it was only 1,5 weeks old and easier to sell. Also I had the impression that the nVIDIA performed better in speed and picture quality than the ATi, but that can be just type-related.

Now the thing: I gave the good quality (expensive) VGA cable to my son who uses Debian as well because this cable had given me a markedly better quality picture on my monitor. He swapped the cables and his normal 19" screen wasn't detected anymore and gave only some low resolution and vague picture!
I checked the pins of the cable and all were there. No breakage, no nothing!
I know with digital cables there are a few different types, but with VGA I didn't expect anything of this, especially as this was a professional type cable with all the pins there.

So my ASUS monitor was probably also not to blame for this problem.

I do not understand how this can be, but I thought it was a good idea to let all you friendly guys know that this sort of crazy thing can happen and puzzle you for months.