If cleaning the lens didn't fix your disc reading issue, a number of other issues may be the problem. The lens may be out of place, or perhaps the drive has simply burnt out from age (unlikely unless you played your Wii quite a bit).
Odds are you'll need a professional to repair it, regardless of what the issue is, unless you've a lot of experience tinkering with electronics yourself. Nintendo offer repairs, but they aren't at all quick and can be pricey. Contrarily, some stores may offer unofficial repairs. Cheaper 'n much quicker, and often just as reliable as Nintendo's.