It's solved now. Here's more info.
In the meantime I've had two sessions with Autodesk support, each about 90 minutes. The registry has been checked, and some other attempts were made.
No solution after all, besides an advice for buying a new PC. I must admit, that it's been bought in 2011; it's time for thinking about that.
But in the second session, the support person made a comment, that it's been a big step from Windows 10 1903 to 2004. It's correct, but these Windows updates are coming in here without any notice before. Perhaps someone knows how to get more control about that.
Problems began after 2004 update, and I switched back to 1903. Some issues were solved, but not all Autodesk updates could be applied. Trying Inventor Reset Utility, repairing and uninstalling made it still worse, and ended in no more success of re-installing. I've made many attempts for permissions to the faulty key in Inventor setup, but nothing helped. A similar experience showed up with Revit 2021.
Yesterday after the second support session, I began thinking about the step from 1903 to 2004. The intermediate version 1909 was not really easy to find, but I got a download in the end from here:
https://www.heise.de/download/product/creators-update-windows-10-update-assistent/download
Several hours later and after a long delay at 27% of install Windows 10 1909 was on my PC. Inventor 2021 and Revit 2021 could be installed back, together with all updates.
Final thanks to Rainer Hotter (Autodesk Global Support at Munich) for the "big step" hint .
Walter Holzwarth
