For testing purposes try to work from another copy of operating system, another computer and, if possible, using another network provider. E.g., you can check your website from one of Internet clubs as they meet all the mentioned conditions.
If you do not have such possibility, then it is desirable to do the following actions step by step:
1. Disable your firewall, antivirus while running diagnostics;
2. Disable the traffic saving services (e.g., Traffic Compressor);
3. Disable the torrent client or any other services that can create a lot of connections, if any;
4. Try to use another browser or update the current one. Maybe some necessary browser functions are disabled or are working incorrectly. If your Internet Explorer version is less than 8 – install latest Windows updates, or install Internet Explorer 8 as a separate package; if you use Opera version less than 10.60 or Firefox less than 3.6.3 – update the browser.
5. Make sure that cookies are accepted by the browser, clear the cookies history; check whether JavaScript is enabled in your browser; clear the cache (temporary files) of the browser. You can find the information on how to do this in the "Help" tab of your browser.