To me, what I think this song means could be 2 different things.
It could mean what Joel went through, and what his depression was leading him to do. To have thoughts of not wanting live, to just get out of the world, but he soon realized his life has meaning, "please tell me I'm not undone" could mean his life isn't finished just yet. Joel is living his life to the fullest and never gave up.
This song could also mean how some people feel when they are depressed. They start doing things to recover from it, such as the drinking, or it could be anything. It also explains how some people feel a certain from the inside, emptiness and feel like no one cares and then they begin to consume themselves with negative thoughts.
To me, what I think this song means could be 2 different things.