There are lots of examples of artists blowing up without labels (though some subsequently start their own or get signed) in the past few years by distributing their music on the internet for free. See: Pretty Lights, Girl Talk, Odd Future, The Weeknd, Justin Bieber, etc. It won't be viable for every artist/band but neither is the music industry of old. You must bring something special because otherwise nobody will care.
It's not clear the internet has actually improved the odds, though. There are plenty of examples of artists DIYing their way to at least moderate prominence decades ago as well; particularly common in punk-rock, where you've got Bad Religion, Fugazi, Crass, etc. You didn't have blogs to promote your music, but did have zines, flyers at shows, college radio, etc.
