We did a complete reinstall with Advanced Options - moving all our old files into a folder called "My Backup", and thus found 50 trojan horse viruses in AVG. We now seem to be virus free, and Spybot and AVG are not finding anything; we no longer have any of the behaviors of a system with viruses. We have Spyware Blaster and ZonedOut installed, and are in the process of getting a firewall. IE security settings are on "high". I think we can safely call this "closed"
Thank you for all your help, Ried. You are absolutely fantastic, and have helped solve many problems this week. I greatly appreciate your effort put into this problem!

