We are making progress! My PC is now behaving normally.
As you will see from the logs, I ran BitDefender and
HJT twice. The first time, it found a malware and a trojan. The malware seemed «attached» to Panda Antivirus.
I uninstalled Panda (which I do not really like...) and ran BitDefender again. The malware was stil there, hidden somewhere else... No trace of the Trojan.
I suppose we will have to go for another round of actions to get rid of the resilient malware.
Which Antivirus would you recommend that I use afterwards?
Thanks again for your support!