The problem isn't the computer, it's the Worms configuration. It burps when there's a router (especially linksys) with more than one computer attached, and it can end up disconnecting all computers.
Go into Network configuration (in Worms) and set "Force IP Address", if it isn't checked. If that doesn't work, pull up the text file datarate.txt (should be somewhere in the Worms directory structure, unless Worms put it in a system directory) and set the datarate to 8-10K.