Hello Jari,
Thank you for providing the zip file, and sorry for taking so long to respond, but I have been having difficulty analyzing the problem.
I can only reproduce the issue you are having if I somehow prevent my system from accessing the web address we need to access in order to perform a login, so I think Fusion is having trouble accomplishing this critical step on your system.
However, while I told you to omit any of the demonstrated files or folders from the archive if they were not present, I'll have to admit I did not expect both "Autodesk Fusion 360" and "Web Services" to be missing from your system. Without one of these folders (particularly "Web Services"), I cannot tell what web address the system is actually trying to use to establish the connection so that we may investigate more thoroughly.
I am thinking that there may be some discrepancy between where I asked you to look for files and folders, and where Fusion is actually putting them, so may I ask you to run another diagnostic?
In your windows command prompt, issue the following command exactly as presented:
powershell -C "[Environment]::GetFolderPath('LocalApplicationData');$env:LOCALAPPDATA"
And report how many lines of text are shown and whether they match or not.
If there are two lines, and they do not match, please repeat the process for collecting diagnostic files in the folder indicated on the first line.
If this doesn't work in getting us the information we need, we may need to consider other alternatives.
Thanks,
Steven