I have exactly the same and had same problem. I had previously set up the networked machine to use the dial up connection via the proxy server.
I found out that the broadband would only work on the networked machine if all pcs had 'set ip address automatically' set and the check box for the proxy server was unchecked. the lan settings also needed to be detect automatically. I suggest that you check these out first. When I got it sorted it all worked fine - in fact I'm quite impressed with the Bt broad band!