Wii Error Code 51400-51499 - Wii Error Codes

This error is caused by an issue with the Wii console being unable to connect to your wired router.
To solve this error :

Try changing the channel of your wireless router to either channel 1 or channel 11 which can increase download speeds. Be sure to test both channels to see which works better or faster.
Log on to your router by using the default IP address and check if MAC filtering is on or enabled, which is usually under Security. If MAC filtering is on or enabled, add the Wii console's MAC address as an approved MAC address.