My neighbour had this same problem with a Wii he got for Christmas except worse than you. Couldn't get anything to run for long.
It's a hardware issue and you'll need to contact Nintendo. They are usually very good for returns (returned a couple defective wii-motes). They have an option where they'll take your cc # and then ship a new Wii, once it arrives you send the old one back at no charge to you, but of course if you don't ship one back they charge you. Or just do a standard return.







