I've had limited connection issues over the last couple of days, which is why I aske you the questions I did.
My solution, and it seems to work, is to go into the Wii menu and confirm all of your connection settings and perform the connectivity test under "Internet."
Also, you can check your PC. If you have the Wii Connect 24 enabled (which you should) in Windows XP a message will pop up every few minutes to let you know that a user is connected to the Nintendo Wi-Fi service. That's your Wii. I like seeing the message because it's sort of assurance.