Hi Deepak Kori,
thank you very much for your Response!
This was actually the deciding hint!
I searched my registry for the string "maxdb" and deleted all entries.
Then I deleted the Installation Folder and C:\Users\MyAccount\sdb manually. I also removed the program from the program list.
I ran a registry cleaner Programme and rebooted my machine.
Then I reinstalled Database Studio and started it as Administrator.
And finally: It is running fine now!!
Thank you so much!