Troubleshooting Wii Error Code 51330

Getting the Wii Error Code 51330 can be very frustrating, but the good news is there are several fixes that should clear the problem, all of which can be done at home. Chances are, your console does not need any repairs or replacements. Just follow several troubleshooting steps to locate the exact problem and you will soon be playing again.
As the error states, the wireless security pass code for your home network may have been changed or is entered incorrectly on the Wii console. In other words, a firewall in your router is blocking access. This most likely means the security settings in your Wii do not match those your wireless router has been set to allow.
This can be as simple as entering the wrong WEP or WPA key, so double-check to make sure it was typed correctly. You can find it under the “wireless security” section of your router settings. If that is not the problem, next check to see if the MAC Address Filter is enabled on your router, and if it is, add your Wii's MAC address to the list of those allowed. To find this address go to your Wii's Settings, Internet, and Console Information page. You may also need to input your IP and DNS settings manually if they were not automatically detected.
If that does not work, there are other settings to check. Try changing the channel your wireless router broadcasts on to either 1 or 11. You should also change the mode on your router to Mixed if it has been set to G Only. Wii is only compatible to WPA2 AES, so make sure you do not have your router set to WPA2 TKIP. While fiddling with the settings, you might also want to change the name of your router to something less generic, in case other similarly named routers nearby are interfering with your connection.
If you have not tried it already, power cycle your modem and router. To do this, unplug both of them and wait a few minutes. Plug the modem back in and after waiting for it to initialize, reconnect your router. Check your Wii console and see if it now connects.
Other solutions people have reported include removing old Game Cube memory cards and laying your console flat rather than upright on the stand. It is also possible you will need to update firmware.