Wii Error Code 51331 means there is a problem with wireless security.
Make sure your router’s WEP key matches the WEP Key you entered in the Wii.
If your router is using 64-bit encryption, the WEP Key must be 10 characters.
For 128-bit encryption, the WEP Key must be 26 characters.
WEP Keys can only use the characters 0-9 and A-F.
If your router allows more than one WEP key to be entered at a time, make sure the key you’re using is on slot one.
If you double checked the WEP or WPA key with the router and the Wii and they match, but you still receive the Wii Error Code 51331, then MAC filtering may be enabled in the router. You will have to add your Wii’s MAC address to the router’s allowed list. You can do this by logging into your router and going to the “access control, access list, or network filter” settings.
If you still have trouble with Wii Error Code 51331, try changing the wireless router’s channel to 1 or 11. This may increase download speed.
Check Nintendo’s router page
for special notes on your router if available. Follow the instructions of the special notes.
Your wireless router must broadcast in mixed or b/g mode and cannot be set to “g” only mode.
If you still encounter the Wii Error Code 51331, try doing manually setting up the Wii’s internet connection. You can find your network information to enter into the Wii by doing this:
On your PC, click “Start” and then “Run.”
Type “CMD” into the field that appears to open a new window.
Type “IPCONFIG/ALL” and press “Enter” to display a list of internet settings. Locate the settings asked for by the Wii console during the Manual Setup process and enter them.
Power cycle the wireless router and modem by unplugging both from the wall. After waiting a minute, plug the modem back in and wait another couple of minutes for the modem to initialize. Plug the router in and wait for the router to initialize. Now try reconnecting the Wii to Nintendo WiFi Connection.
Hope this helps a little