Third step after successful pinging a machine and having already checked the proxy settings of the browser (don't forget to check how they are set at the machine where it does work) would be to actually trying to connect on the correct port with telnet. You don't need to understand the protocol, usually it's enough to see whether a connection can be established or not.
From the command line, type
telnet www.google.com 80
Where 'www.google.com' is the name of the site you want to connect to and '80' is the port - I assume you're trying to access the web interface, so that would be 80. Expect one of:
Connecting to www.google.com...Could not open connection to the host, on port 80: Connect failed
Means the connection couldn't be made by any reasons: the port might be closed, a firewall might be blocking the request, the host name might not be found, or the remote machine not be reachable. Yeah, rather unspecific, that's why you try the ping first.
If the screen blanks (WinXP telnet.exe does this, Linux does not) and it seems like you can enter something (cursor moves), the connection seems to be fine. Don't worry if you don't see your cursor anymore, don't see what you type or some garbagge is printed - just close the window.
If the connection doesn't work, look for personal firewalls.