While I was following the steps to get Wiimfi + Competitions working, I opted out and opted back in again to Message Board notifications for Mario Kart Wii (that was one of the steps). Next, I thought I'd see if the Mario Kart Channel works, so I tried to install that. Before it installed, I was booted back into the Wii Menu (the Mario Kart Channel wasn't there). I didn't see it as any real issue, so I continued with the tutorial. Next, I patched the Mario Kart Wii ISO, which seemed to work fine. After loading the ISO, the safety screen loaded up fine before going into a black screen. After this, I tried loading the unpatched ROM and it had the same issue, and even loading the home menu black screened too. I have no idea how this happened.
EDIT: I just reinstalled Dolphin and that worked.
EDIT: I just reinstalled Dolphin and that worked.