|I did all kinds of scans using all kinds of scanners (AdAware, SpyBot, Avast, Symantec AV, etc.)|
It's a fresh installation and it was no wonder that there were no any malware/spyware/virus/trojan infections.
It's a clean PC.
Still, my internet connection only works OK in Safe mode with networking.
I stopped most processes, stripped the Windows down to its bones - no result.
It keeps messing up the connection when in normal mode.