You can try an official Wii lens cleaning kit. With the way it gradually stopped working, it's very possible that a big ol' hunk of dirt got lodged over the lens. If it doesn't fix the problem, it's never a bad idea to have the cleaning kit. Cleaning it every so often would probably help prevent malfunctions in the future.
Failing that, you should call Nintendo about your issue as opposed to setting up a repair through the website. The price of a repair is negotiable, so if you talk about things like being a big fan or never having issues before, you might get a discount. No guarantee it'll work, but it's worth a shot. Also, if you have Super Smash Brothers Brawl and tell them that it doesn't work in your Wii, they may even fix it for free. I've heard of people doing this.
Unless there's something else wrong with your Wii, you will not lose any data from this repair. All they are going to do is replace the disc drive, so your data will be safe. If you want to be cautious, some save data can be copied to an SD card, but there's actually a lot that cannot. It isn't just limited to games with online modes, but also games with create modes, and other games are just a mystery. Miis can be stored on your Wiimotes, ten per Wiimote. Your Shop Channel account would be transferred if they sent you a replacement, so no worries there.
For me, it took a full month to get my system back, but it would seem most people get faster service. You can check the tracking/repair status daily on their website.