That is indeed strange, sure sounds like there is a firewall or something blocking on some port. I don't know that the connection uses different ports after the initial loading files.
The browser goes through three screens, "Loading Files", "Loading", and "Loading System Settings", so it sounds like you are getting stuck in the first one, is that right?
I didn't have to set up anything on my browsers to get it to work fine. I use a router for the DHCP server and an unmanaged switch to connect my network. I can control the RX-V3900 from my Mac OS-X, Windows XP and FC10 (Linux) boxes, using IE6, Firefox 3 and Safari, no issues on any of them. (Sorry, I don't have any Vista machines). Your trying so many machines doesn't sound like the problem would be in your machines, if you do indeed keep them up to date, including Java (usually automagic in Windows).
I do have firewalls turned off on all machines (since this is all behind my firewall/router).
When you said you tested with only the PC and the Receiver in the net, was that still through the switch? I'm not familiar with managed switches, but perhaps if it was in the net between the two, is there a way to try without it? If your router has more than one local LAN connection, perhaps plug a PC with firewall off and Receiver directly into the router to eliminate the switch. Or try a hub or unmanaged switch for a test.
I'd recommend setting it up and testing both mp3 and net radio, confirm from the GUI that the IP, gateway and netmask are all correct and that the IP doesn't conflict with any other devices on the network. Also verify the Mac filter is still turned off. Make sure the receiver is powered on (unless you have set "GUI Menu->setup->Network->Network Standby" to on). Then try the browser access to the Receiver. If that doesn't work, then it is suggesting you have a bad receiver.
One other thought that occurred to me is if the Receiver sets any cookies in your browser. I don't know that it does, but you might look through your browser for any and clear them, possibly they got set wrong when you tried it initially with something not right in the network? Just another possibility. I have a lot of cookies that contain some reference to yamaha in my primary browser.
Have you sent Yamaha a support e-mail? They have responded pretty quickly to me when I've sent them a description of my problems.