Tefillah has the power to break through the Heavens and arouse Hashem's mercy, as is seen from the following story:
About 150 years ago, there lived in Europe a gaon named Rav Yeshaya Bardaki zt"l, who was a student of Rav Chaim of Volozhin zt"l.
Rav Yeshaya longed to move to Eretz Yisroel. He first sent his wife to prepare for the family. She sent a letter, informing him that she had arranged a place to live and the like, and he set off with his young son and daughter on the journey. They traveled on a boat with 16 other people.
After two weeks on the ocean, they encountered a storm. The ship was thrown about by the waves until it was finally ripped apart. Rav Yeshaya took his two children on his shoulders and began to swim. After a while, his strength gave out. He thought to himself: If I keep going like this, my children and I will all drown. The only way I can continue is if I let go of one of them and put the other on my back. He began to think about which one of his children he should leave behind and which he should save.
He recalled the Gemara (Horios 13A) that speaks about who takes precedence when it comes to saving lives. It says that a Kohen takes precedence over a Levi, a Levi comes before a Yisroel, and a son comes before a daughter because he has a mitzvah of learning Torah. His daughter accepted his ruling and began to recite Shema Yisroel. Rav Yeshaya urged her to hurry, as his remaining strength was waning. She put one hand in the water and was about to let go of her father with her second hand, when she began to panic and scream, "Tatte! Tatte! Have mercy on me! Don't let me drown!"
Rav Yeshaya later said that he had never heard a scream like that in his life. He was filled with love and compassion for his daughter. Even though he had no strength, he picked her back up on his shoulders and decided to try to swim as much as he could.
His daughter's screams seemed to give him new strength, and he swam some more, until he saw the shore in the distance. After much exertion, he reached the shore, where he collapsed on the ground with his children.
When he felt a bit revived, his daughter thanked him for saving her life, and he responded, "It wasn't me who saved you. It was you who saved me. I had no more strength left, but your cries gave me the power to continue swimming."
R' Yeshaya made it to Yerushalaim. When he related that story, he added, "Hashem caused this to occur in order to teach me a lesson. Even when we have no merits, and it seems like Hashem, so to speak, has no strength left to save us, we can still cry to him. If we scream, 'Tatte! Save us!', He will be filled with love and compassion for us, and He will find a way to save us."