What does Hamlet's first soliloquy tell us about his depression? Does he feel isolated in his grief? "O that this too too solid flesh..." Act I...

This is Hamlet's statement that he wishes he were dead, that his body, all too physical, could just melt away "into a dew" or that God had not forbidden suicide, "fixed his canon against self-slaughter" as he will say later.  He has lost all interest in the things of this world ("weary, stale, flat and unprofitable" says it all).  What was once, by implication, a flourishing garden is now gone to seed with only things "disguisting and decaying" growing there.

This tells us that his depression is very serious.  It also tells us that he does feel very isolated and alone in his grief: "an unweeded garden / That is going to seed."  He has lost interest in the things that once gave him pleasure (a classic sign of depression), and he is contemplating suicide, stopped only by the fact that he just can't "disappear," and that God has forbidden him to act on his desire to die.  And this is a theme we will see developed in other parts of the play.