Just found a new nasty infection: XP Defender.
It looks similar to infections like “win antivirus 2007” and “win antivirus 2008” etc.
I tried to remove it by booting my UBCD4win CD, updating superantispyware, but the scan revealed nothing wrong with the infected PC.
Next, I started in safe mode (with networking)… by pressing F8 when the PC is starting, and I was able to install (and update) malwarebytes, and it fixed the PC very quickly.