Lan Network Problems (by 2 users)

Hi, I have a problem between a Desktop and Laptop. Sometimes if my Laptop's WiFi isn't working, meaning finding any Networks I hook it up to my dads Desktop through a LAN Cable. His Desktop is a 2007 HP Pavilion a133On running Microsoft Windows XP Media Center Edition, My laptop is a IBM ThinkPad T40 running Microsoft Windows Vista Home Basic. He still uses Dial-Up and Like I said if my network isn't working right I hook it up to the Desktop. It was working fine last month, and all I had to do was plug the LAN cable in and I was connected. Now When I plug it in today, My laptop detects the Desktop but the Desktop don't detect my Laptop. On the Desktop it shows the LAN Connection with a yellow ! icon saying "Limited or no connectivity" and on my laptop the icon just shows two computer monitors saying "Unidentified network" If I was connected it would show a Earth Ball icon that is letting me know I'm on the internet.
I don't know if it has something to do with Windows XP Service Pack 3 or not because Last month it worked and Service Pack 2 was on it. But on my old desktop I use to have, had Service Pack 3 and I connected my laptop and it worked fine.