http://www.nintendo.com/consumer/wfc/en_na/ds/results.jsp?error_code=51310&system=Wii&locale=en_US
Unfortunately, but Nintendo's Error Code Lookup feature can't seem to find the 51310 error code so it only gives general tips on how to correct this, sorry.
However, have you tried power-cycling your wireless router then set up a new connection settings on your Wii console?
NOA_TECH_JAKE wrote:
This could indicate there wireless interference preventing the Wii from seeing your router. Typcially, this can be resolved by changing the channel the router is broadcasting on. We recommend using channel 1 or 11 as they tend to have the least amount of interference. If neither of those channels work, you will want to go through the rest of the channels one by one. If you do not know how to access your router settings to change the channel, you can follow the link below and select your router from the list. Here's the link:
http://www.nintendo.com/consumer/wfc/en_na/routers/index.jsp
You will also want to make sure the router is broadcasting in a mode that is compatible with 802.11b and 802.11g.
If you continue to experience an issue getting the systems to connect with your router, you should call our Consumer Service office. They can be reached at 1-800-255-3700, 6am-7pm Pacific Time, seven days a week.
And if that didn't help, perhaps since your console can't seem to find any access points, it could be some type of wireless interference such as what NoA_Tech_Jake posted on another thread, and suggested changing the router's channel and broadcasting mode.
