After running Spybot, the spyware Spynet was not removed at first try.
So I had to restart windows in Safe Mode and thanks to the posts about Spynet I was able to zero in the file c:\windows\system32\winlog\Winlogon.exe

What I did was go to the directory c:\windows\system32\winlog\ via safe mode command prompt, because the file is self-regenerating when deleted, but no file can be created in Windows if a file exists with the same name. It's the oldest spyware trick I know, but still true .

In the command prompt, type this:

cd c:\windows\system32\winlog\
attrib -s -r -h Winlogon.exe
del Winlogon.exe
attrib -s -r -h winlog
rd winlog

copy con winlog
^Z (<ctrl-z>) <enter>
attrib +s +r +h winlog

Then I restarted the system and did the Spybot check a second time. This time the spyware was finally removed and I found no other trace of it, although I think there may be still a backup of the spyware somewhere, but AVG didn't detect anything since. Mcafee antivirus never cought anything (I'm thinking about switching to AVG free now and not renewing Mcafee).

Thank to everyone. Keep up the good work