I'm getting an Error code 51030 when I'm trying to make a wifi connection on my wii console

This error code has to with a connection issue with your wireless network. Here is the link to the Nintendo support page that deals with this error code:
http://www.nintendo.com/consumer/wfc/en_na/ds/results.jsp?error_code=51030&system=Wii&locale=en_US

Nintendo Customer Service Nintendo Wi Fi Connection Error Code Results

Click above link for resolution. :)

Have you set up your wifi connection? The Wii connects through a wireless router connection.

Error number 51030 mean that there is no wireless network that is within a range of your WII console is either configured into it or is compatible with it and your WII console will try to do anything that does requires an internet connection. This could mean that the password could of have been changed or was configured incorrectly on the console.

Try unplugging your router for 10 seconds and plugging it back in. This will cycle the router. If that doesn't work, try erasing the connection settings completely from your Wii and trying again. Hope this helps!

You must retype in the code for your Wii. Follow the instructions on this page
http://www.ehow.com/how_5114771_set-up-wifi-nintendo-wii.html

Hi there!
Error code 51030 means you cannot connect to your wireless network.
SSID (Service Set IDentifier) is the "name" of your wireless network. You'll have to make sure that you are connecting to your own wireless connection and if you don't have one, then you'll need to setup a wireless network.
Hope this helps.

Sorry to hear you are having problems with your wii. According to Nintendo, error code 51030 is:
"Error Code: 51030

Unable to connect to your wireless network"

Make sure your wireless network is set up correctly with the correct SSID and encryption key. You may also just need to power cycle your router.

For more information, here is the official support article from nintendo for this error:
http://www.nintendo.com/consumer/wfc/en_na/ds/results.jsp?error_code=51030&system=Wii&locale=lang

error 51030
http://www.nintendo.com/consumer/wfc/en_na/ds/results.jsp?error_code=51030&system=Wii&locale=en_US
means that your wii is having trouble connecting to your wireless network.
please make sure that you wireless network signal is in range of the wii
setup your wii with wifi by going to the wii button on the home screen
wii settings> then page 2 select the internet.
go to wireless connection and connection 1 to setup your wifi.
search for access points and input the wireless security password to connect to the wireless network.
if this worked and you still get the error code please power cycle the wii and also check your wireless connection settings and any interference from other wireless networks. you may need to change the channel for the wireless network to 1 or 11.

This might be handy: http://www.nhotspot.net/wii-error-code-51030/ and http://www.wiierror.com/wii-error-51000.php
Try adjusting the "Channel" your wireless router broadcasts on. We highly recommend setting your wireless router to either channel 1 or 11. This can potentially increase the download speed.

Verify that the proper Connection File (1, 2, or 3) is selected in the Wii System Settings.

If you have multiple connection files setup, and you have recently received a system update, it is possible that the update has caused the Wii console to select a different Connection File. Click here for step-by-step instructions on viewing your connection settings.

Make sure that your network's name (SSID) matches exactly to what you have entered in the Wii console's settings.

Log in to your router using the default IP (consult the router's owner's manual for assistance).

Look for the section for SSID (typically in the "wireless settings" area).
After you find the SSID (network name), verify in the Internet Settings of your Wii console that the SSID is appearing exactly as listed in your router. This includes making sure capitalization, spaces, or special characters match exactly.