Internet Explorer

UPgrading to ie6 you will probably find the same problems. Your security settings will remain the same. This sounds more like an issue in your Internet Privacy Settings.
From a browser, click TOOLS>Internet Options>Privacy if the slider is the Top (restrict all cookies)bring the slider down a little to accept cookies. This can be adjusted to allow all cookies or just from trusted sites, you will probably have to play with it to find a setting that uses a privacy level that adheres to your company policies. Secondly, check the security tab and you can customize it to allow sites that you know are secure and allow users to visit.
OM

How do you connect to the internet?

Have you got the correct port allowing HTTP traffic throughput.

As above I don't think upgrading will help sound more of a security or port setting issue, of the top of my head I think Port 80 is HTTP. (don't shoot me if I am wrong ;-)