http://www.nintendo.com/consumer/wfc/en_na/ds/results.jsp?error_code=51340&system=Wii&locale=en_US&action2.x=9&action2.y=30 said:
Error Code: 51340
The Wii console is not able to connect to Nintendo Wi-Fi USB Connector.
1. Check for interference.
1. Check the location of your PC/Wii console
If possible move the PC and/or Wii console away from walls and off the floor, and try to place them in a central location in your home. Also, try to keep them away from metal objects such as metal filing cabinets which can cause interference.
2. Attach the extension cable to the USB Connector
his helps to move it further away from hardware in the PC that may be causing interference.
3. Wireless noise
Noise from Cordless devices (cordless phones), or wireless electronics (wireless keyboards, headphones, cell phones), especially those using the 2.4GHz frequency, can interfere with your wireless signal. In addition, older microwave models can cause wireless interference.
2. Try uninstalling the Nintendo Wi-FI USB Connector software, and re-install. For step-by-step directions, including a link to the latest software, click here.
3. Does your PC have any security programs (firewall, anti-virus, anti-spyware, anti-adware, etc.) installed? If you are using the Nintendo Wi-Fi USB Connector, and have a software firewall or other computer security program installed on your computer, there may be additional steps you must complete to allow a successful connection.
"Trusted" Applications:
If your firewall or PC security program keeps a list of trusted applications (also known as a "trusted zone"), the following programs are installed with the Nintendo Wi-Fi USB Connector, and require internet communications. If prompted by your firewall or PC security program, add these to the list of trusted applications. This information may also apply to certain computer security applications, such as anti-virus, anti-spyware, etc.:
o Nintendo Wi-Fi Connector USB (NintendoWFCReg.exe)
o Setup.exe (when installing the USB Connector)
o SoftAPInstDrv.bin
o mdriver.exe
If you are still receiving this error code, it is likely that the Nintendo Wi-Fi USB Connector is not compatible with your current home network.