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Wii Error 110213
The error appears after updating the Wii using WiiConnect. The error message that appears reads "Error Code: 110213 There is a problem with the WiiConnect24 service. Please try again later."
Nintendo asks that you call them at (800) 255-3700. The gamer who encountered the error 110213 was told that this was an hardware error and that he would receive a new system. The only thing that is not working is WiiConnect24 which means you will be able to play all games but not be able to upgrade the Wii.

Currently, Nintendo has two options in place to resolve the problem. If you do not have any data saved to your system that is important to keep, then you can contact Nintendo customer service and they will ship a new console to you in 3-4 business days. However, if you do have important data saved to your system, then things get a little trickier. Data like game saves and Miis are not disastrous to lose, but Virtual Console data is. While Virtual Console games are re-downloadable should you delete them, the data saved on your console regarding which games you have downloaded is tied to your system. In this situation, option #2 is the way to go.
Option #2 requires that Nintendo send you a shipping label which should take 4-10 business days. Once you receive the shipping label, you can use it to send the console to Nintendo for repairs, after which they will send it back to you. Sadly, this process takes 8-12 business days, meaning that if you choose option #2, you will be Wii-less for a good long while. source
If you reformat the disk the system might be able to connect to Wiiconnect24 again. (taken from the comments from the link above)
One Gamer reported that a manual reboot did help to complete the update. (taken from the comments from the link above)