Been a l-o-n-g time since I used System 7. Look at this link http://support.apple.com/kb/HT2344 I'm thinking that you have a "bad" extension. You might try an intentional Rebuild of the Desktop at startup & see if that solves the problem. Another thing to try. Startup with the Shift key depressed. This turns Off extensions - now do you get the rebuild message. If not, use the Extension Manager to turn Off extensions until you find the offending one.
Thanks for your recommendations I have followed so far: intentional rebuilt of desktop, skip extensions - but without any success. FirstAid and Norton do not find any errors. Still after each startup the desktop file will be rebuild. The new 2GB HDD I have initialized with a patched "Apple HD SC Setup 7.3.5".
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Argl!! I am banging my head! So stupid! I found it. In the root directory of the HDD I created a folder named "Desktop". After renaming it everything works fine!