7404VNPX Raspberry Pi Slows Down Internet Access For Whole Network

Whenever my Raspberry Pi is connected to the network (via ethernet) the entire network is slowed to a crawl. On my main computer, ping times for google.com go from ~10ms to ~200ms and it takes forever to load web pages. Connections are also slow on the Pi, with an apt-get update showing pathetic speeds in the order of 1KB/s. Turning off the Pi completely removes the drag from the network. Interestingly, the local network appears to be fine, with scp copying files at reasonable rates; around 4.5MB/s to the Pi.

I've tried static and dynamic IP addresses for the Pi, but both have the same problems. Switching from Raspbian to Arch also had no effect.I've checked the connection's duplex with dmesg | grep -i duplex, which shows that the Pi's connection is running at 100Mbps, full-duplex, as expected.

My modem/router is a Billion 7404VNPX (an Australian thing); relatively high-end, albeit a bit buggy at times (it will occasionally delete all its firewall settings). It assigns IPs in the range 192.168.1.1 to 192.168.1.20 and has 192.168.1.254 as its own IP. When I assign static IPs I tend to use the 192.168.1.200 area. I recently tested the connection with the Pi plugged straight into the modem (rather than via a wall socket) and it managed to crash it entirely!