Both IE and FF support add-ons. Try accessing the web site with all add-ons disabled. Run it in default mode, using all standard defaults for system values. Another problem is that configuration might have been tweaked.
Proxy server settings, and particularly net mask for proxy server? They're a little more obscure, and if things work OK on the intranet, but not on internet, it might be a possibility. You might also try TRACERT and see if the route is the same for both the good and bad machines.
If that doesn't work, check network settings for the affected machine, both on the machine itself and in any servers/routers/bridges/gateways along the way.
And finally if all else fails, try reinstalling windows on the affected machine.