I loaded the newest Radeon Driver and tried again. The upgrade procedure to Windows 8.1 was very long with many reboots. It looked like a neverending loop, always the same screen, but after 4 or 5 repetitions it came to a successful end.
However, it could be the AMD Radeon driver, but maybe Microsoft did some improvements since my former try and that's why it worked.
I can only say: Try it again, but plan enough time. Maybe you need to run the upgrade 2 or 3 times with updating drivers. This will take hours.