The past is what creates the Emily we come to know in this story. Her father is a big catalyst into her character. As she was maturing, her father chased away all suitors claiming that they were not good enough for her. Because of this and his unexpected death, she is left alone and poor. No one is there to take care of her, and most likely never will be. In fact, when her father died, she was in such denial that she left him there in that same spot he died for 3 whole days.
Emily probably could have eventually married and been all right, but when the love of her life (Homer) comes into the picture, things change. He is a roamer. He never plans to stay anywhere, and Emily knows that she can't have another man leave her ever again. So the loss of her father is what creates who she is and affects her decisions, even when they are murderous thoughts. She then poisons Homer so that he could be with her forever (even if he is a corpse).