If one browser works but others don't it is more likely to do with firewall settings than the internet connection.
Also there may be configuration settings in the browsers that are incorrect - like trying to use a long-defunct dial-up connection instead of the broadband connection.
It could also be malware, but I would expect IE6 to be the first to fail, not the last if malware were to blame!
Possibly the most sure-fire way to get everything running properly is to back up all your data, reformat the disk and do a clean install of your favourite operating system.
SD