I'm always nervous when hacking around in a computer's registry so I backed everything up yesterday before trying this but, happily, I have fubared nothing. I now know how to get to the registry editor in Vista, and through the magic of regedit and adding a new key value, my machine in the study now can see the router and access the Internet rather than insisting it can only see the local network. Which means I don't have to go sit in the living room with the other laptop whenever I want to answer e-mail or connect to Arm.
I know that's small potatoes for the people trained in network admin-ing, but I feel pretty damn good about it. *flex*