What two moments in Death of a Salesman vividly convey Willy's desperation?
For me, I would have to pick firstly when Willy is fired from his job in Act II. His sheer desperation and fear is conveyed when he grasps Howard's arm and cries out "Howard, you've got to let me go to Boston!" Willy realises that if he is fired he is literally nothing and all of his dreams and hopes have come to naught and he will have to face the reality of his own failure.
The second instance is at the end of the restaurant scene when Willy returns to reality after his flashback and finds out that his boys have deserted him and left him alone. He asks Stanley where he can find a hardware shop to buy some seeds:
I've got to get some seeds, right away. Nothing's planted. I don't have a thing in the ground.
This conveys his desperation because seeds in the play are symbolic of hopes and dreams and also reflect on how Willy brings up his children to accomplish great things. At this point in the play, Willy realises he has nothing: he has been fired and his son's plans of getting a loan from Bill Oliver has come to nothing. Willy literally has nothing left to hope for. We are presented with a man who has been stripped of everything and who has had all of his illusions and dreams taken from him cruelly.