ILOTS: If the system is new, get the card replaced. Nothing should be frying itself that fast unless you massively overclocked it. The company that made the card needs to send you a replacement right quick. Don't take no for an answer.
8onus: If you have a router, whether you're connecting to it through wireless or not, it probably has to be configured to specify which PCs on your internal network will receive forwards of incoming information to various ports. I don't know which port limewire uses, but you'll need to open that one up in the router configuration and set it to forward to your computer's IP address. See the router's manual for more details on how to do this, and the settings dialog in limewire for information on which port it uses.