Hold reset while turning on the Wii, a menu will probably appear. navigate into the settings menu, go to system menu hacks and disable the "block online updates" one (should be named something similar to that, if in doubt, disable ALL system menu hacks). After that the update should work.
Although I don't know of any official software for listening to music. Unless you're talking about via the Internet Browser, which I guess would work for some sites at least (although I wouldn't count on it working for all sites).