Check what applications are running on the "problem PC". When this is unplugged - the connection is fine so I would say that some programs (possibly spyware/adware/etc) are accessing the internet with lots of traffic.
(1) on the "problem PC", click start/control panel/network connections.
(2) double click on the LAN connection and see what the traffic is like (packets sent and received).
If this is high then there is a lot of internet/network traffic coming from the "problem pc".