Anti-adware/spyware programs don't tend to cause trouble as such. These are for the adverts and spying programs. the main reason why some sites no longer work is because your
hosts file is filled with local IP addresses for remote server domains. In order to list every site and block all websites, the 'virus' needs to add every possible URL into the
hosts file and point it towards 127.0.0.1 to block it out. No virus, spyware or human can fill this file with every combination of letters and numbers, even for those popular sites.
If this has gone over your head, simply remember to get hold of
Spybot's Search & Destroy or
Lavasoft's AdAware to search for and remove most spyware. That way, little to no spyware will survive for long. Try to use both for ease of mind.