If your Wii has more problems than just a buzzing noise, you might be able to get them to fix it for free if you can convince them that your problem is related to the newest system menu 4.2 update.
My out of warranty launch Wii was set up as a "warranty repair" but it had a few different problems. The problem that I always had with it since December 2008 (out of warranty by then) was that my games would freeze, but I just kept on playing with it since I didn't want to pay Nintendo to repair it. After I upgraded my system menu from 3.4 to 4.1, I started having different problems (SD card related, Mii Channel errors, and games still freezing). Since some of my problems were caused by me updating to 4.1, they set it up as a free repair, it would have been $75 otherwise.
Plus, a lot of people seem to be having issues with the new 4.2 update, so Nintendo says they'll repair Wiis for free as long as yours isn't modded:
http://techforums.nintendo.com/nins/board/...thread.id=29992Beware though, you might end up getting a replacement Wii in return. That's what happened with me. They couldn't (or didn't even try to) fix my Wii, so they sent me a different one back. They were able to transfer most of my saves from my old Wii (lost my Smash Bros Brawl save), but my wifi enabled games won't let me online anymore because my friend codes were created & tied to my original Wii. They give me error code 60000 when I try to go online with them - from other people's experiences with this error code, the only way they were able to get online again was by deleting their save file and starting all over again.
They also didn't transfer over my address book data or any of my Miis (80+ in my plaza and 600+ in my parade), so I lost all of that too. My friend who sent in his Wii got his address book data transferred to his replacement Wii (they even kept his old Wii number), so YMMV with this.
They did manage to keep my Wii message board messages and all the pictures on my message board, but I don't really care about those.
So, you can try to call Nintendo and see if they'll fix it free. Or if you can figure out what's wrong with it, maybe it might be better to fix it yourself and keep your saved data & everything else.
Or you could go with JDMnAR's solution.