Hello Bytewrangler,
Havent been around in a while but another thing you can check that is if you haven't already is do a traceroute towards your web server with both a machine that works and a machine which doesn't. this will allow you to check if they follow the same path. Another thing i didn't see it mentioned but you dont have a wins server on your network do you? I have seen some strange problems coming from WINS but it would be unlikely to affect your network switches.
I would also check the web servers to see if there is a firewall or filtering on that side if you can.