According to Nintendo's website you will receive that error if you have not entered in your wireless passcode correctly. See below error explanation from Nintendo:
Error Code: 51331
Unable to connect to your wireless network
Likely cause: It appears that the password (also known as a WPA or WEP key) entered into the Wii console is not the same as what your wireless router is set to allow.
How to fix: Make sure the password is entered into the Wii exactly as it appears in your router's settings. Security keys are case sensitive.
Don't know how to find your router's password?
Look for a sticker on the bottom of your router. Many routers provided by Internet service providers have their default password located on a sticker on the bottom of the router.
If you're not able to locate the password here, select the brand of your router below and we'll show you how to access your router's settings.
Hey there. Hope this helps.
51331: this error is caused by the Wii being unable to connect to the access point
So what you need to do:
Try changing the channel of your wireless router to either channel 1 or channel 11 which can increase download speeds.
If your router is using WEP encryption
Unable to connect to your wireless network
This error code is more specific to having incorrect security settings on your wii. Your encryption key is wrong when trying to connect to your wireless internet. Double check your encryption key with your router's settings and try again.
You can see the official support article from Nintendo here:
http://www.nintendo.com/consumer/wfc/en_na/ds/results.jsp?error_code=51331&system=Wii&locale=lang
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