Hello,
Did you uncheck "Reset Winsock Settings" before doing the "clean" mode ? If AdwCleaner had deleted Winsock entries, they should be listed on the logfile and this is not the case here.
I think it'll be helpful if you could do a snapshot of the registry before AdwCleaner's cleaning and after. You can use a software like RegShot ( https://sourceforge.net/projects/regshot/ ).
With the sna...