Wii gets stuck setting up Wi-Fi

I know this sub is inundated with posts about the demise of the Wii Shop Channel. So, I’ll mix it up a bit. For the past...goodness knows how many years, honestly, I haven’t been able to connect my Wii to Wi-Fi, even to download console updates. I’ve had the same issue with two different routers. We got a new router, and it just would not connect. It would see the 2.4 GHz access point and everything, but it hangs on “Testing Connection.” My suspicion is that it’s trying to ping the now-dead multiplayer servers as part of its connection test, and just doesn’t know how to make sense of inaccessible servers. At this particular moment, it’s been testing for about an hour, without throwing an error code or anything. Any thoughts or workarounds?