You can set up your firewall to only let access to trusted websites, but that list is going to be so long that it'll take forever to set it up. You could do it on demand, i.e. allowing requests individually but then you'd have to differentiate between bad and good requests. What you should really do is clean install. Since you're infected and none of the av programs are picking it up you can't rely on any backups.
Just format and start over, it sucks but if you're actually infected with no way to identify the corrupted files you have to just get rid of everything.