WiiSCU isn't working

I have System Menu Ver. 4.0U, with the latest BootMii installed to boot2 and the latest HBC. I updated the Shop Channel not too long ago, but when I noticed my other channels weren't working I tried to update Weather and News channel and they didn't work for some reason. It would say 'Installing the Weather channel' or 'Installing the News channel' or something and just stay there, after briefly saying something like 'downloading ticket' and stay there for a long time, and believe me, I left it running. I tried to install the IOSes in the program too but they had the same problem. I'm using the latest version.

If you currently have the Homebrew Channel, just run it and it should ask for an update. Update that, then update the Wii itself.

Is it safe to update the Wii, though? I thought that would kill my homebrew.

The 4.3 update does not remove the latest Homebrew Channel, but there is absolutely no benefit to updating as the update was intended only to remove homebrew. Anyway, try WiiSCU again and if it still doesn't work, you can download the channels (and their IOSes if necessary) with NUS Downloader. Have NUS Downloader pack these into WADs and install them with a WAD installer.

You could also try dop-Mii.