Marcos, thanks for answering.
I had checked, then cleared, then recreated C:\Windows\Temp folder. Unfortunately that didn't help.
Thanks for telling me about the Process Monitor tool, I didn't know about it. I downloaded it from Microsoft site, filtered all suspicious lines, including this one:
Process: ekm.exe
Operation: QueryOpen
Path: C:\Windows\SysWOW64\%USERP~1\AppData\Local\Temp\
Result: PATH NOT FOUND
The path looks weird enough, but after I had created this folder (C:\Windows\SysWOW64\%USERP~1\AppData\Local\Temp\) activation succeeded. I mark this topic as solved and I thank you again.
Still I wonder why this weirdly named folder was necessary at all.
EDIT: a few typos.