This error is caused by a wireless router firewall issue.
To solve this error :
Try to manually setup the Wii console using your network IP settings.
To do a manual setup of the Wii console using your network IP settings :
On a PC, click Start > Run > type CMD and press Enter > type IPCONFIG/ALL and press Enter. On Windows Vista, click Start > type CMD in the Start Search box > click on CMD icon > type IPCONFIG/ALL and press Enter.
Locate IP settings and use them to manually set the Wii console.
Restart your wireless router by unplugging the power from the wall and plugging it back in. Try to connect the Wii console to the internet.
You may also try to disable the wireless router security or firewall.
Try again to connect the Wii console to the internet.