A problem that serious generally can't be fixed by anyone who isn't mighty skilled at repairing electronics... which is to say, a professional will likely be necessary. If your Wii is still under warranty, Nintendo will repair it for free (so long as you lie about dropping it). If not, the cost could be a tad high.
Some gaming or electronic stores will offer unofficial repairs which generally will be cheaper and quicker. If you're unlucky the repair might be a tad dodgy, but can still be adequate.