I would not say that the music industry is dying. What is happening is that it is changing or better yet, being transformed. In the past (before the digital age) large music labels controlled the music industry. In order to make it as an music artist you needed to be "signed" by a music label and your fate was in their hands. In other words, to produce and distribute your music, you needed a label to make it possible. There were few options (if any) for independent artists. Today things are much different. Though we still have the labels with us, you do not need to have them "sign" you to make it. You can produce and distribute your music inexpensively (and free in some cases) and keep all the profit for yourself.
I think what is happening to the music industry is amazing for artists, not so amazing for the corporations that profit from them.
One trend that I think is not so positive though is the advent of digital instruments. You can actually create music for a whole symphony orchestra (or just about any other instrumental group) without any live musicians. Is it as good as a live orchestra (or any other instrumental group)? Surprisingly, it almost is. I can produce some great sounding stuff just with a laptop and some sound samples. Unfortunately that sucks for professional musicians since there is less and less work for them. In fact, it has become difficult to make a good living as a musician. On the other hand, as a composer, it sure is nice to be able to write for any type of instrumental group and not be concerned with the cost of having it performed or produced.
Overall, the music business is not dying, it's just changing.