Why Doesn't God Answer My Prayer?

Question:  I pray and pray, but I feel as if God is not listening. We always had a good, peaceful family life, but these last years have been tough. We don’t seem to be getting along and our finances have taken a turn for the worse.
I am so anxious about this situation that, not having anyone to turn to, I turned to God.
But God seems to remain deaf to me. Why is that? In addition, what do I say to certain people, agnostics and atheists, who laugh at prayer, saying it is nonsensical and only a figment of the imagination with no real value?

Answer:  God is faithful to His promises, and God promised to answer our prayers. “And I tell you, ask, and it will be given you; seek, and you will find; knock, and it will be opened to you. For every one who asks receives, and he who seeks finds, and to him who knocks it will be opened” (Luke 11:9–10).
If God promises to answer our prayers, He will do so infallibly. But in prayer there are two sides: he who asks and He Who gives.
Our part is to ask. How must we ask?

Saint Alphonsus Liguori, a Doctor of the Church, teaches in his book Prayer, the Great Means of Salvation that prayer must be persevering and humble.

So many times we hear people saying: “Oh, I used to ask God for this and that and the other, but He never gave it to me. Now, ten years later, how glad I am that He didn’t!”
One thing is certain: God will not fail to answer a humble and perseverance prayer. Whether He chooses to grant what we ask immediately or make us wait, we must trust that He, regardless of appearances, is doing us good. What we think is good and what He thinks is good may be two different things: “My thoughts are not your thoughts, nor your ways My ways” (Isa. 55:8), but here is where we must abandon ourselves to His beneficent will. Our part is to be patient, calm and, above all, faithful, because this is the time for testing and later will come the time for full enjoyment.

Answering Atheists and AgnosticsAs for atheists and agnostics, their skepticism proceeds from the fact that they, respectively, deny God’s existence or deny men’s capacity to know God.
In this case, we can only express our regret over their ignorance of this Supreme Being, our omnipotent Creator and loving Savior.
We may direct them to a few sources that may help in their search for the truth of His existence. Atheism and agnosticism can only be sustained in ignorance or ill will because the evidence of God’s existence is overwhelming.
Moreover, God will not hide Himself from those who seek Him sincerely and unconditionally.
Another consideration pertaining to non-believers is this: If God were to grant us absolutely everything we ask at a moment’s notice, such people might start believing purely out of self-interest.
They would look at God as a wand-wielding wizard. And God Our Lord is infinitely more than that. He wants us to know, love, and serve Him for Himself so that He can treat us as children and heirs and grant us unending happiness in Heaven.
"My impression is that the Rosary is of the greatest value not only according to the words of Our Lady of Fatima, but according to the effects of the Rosary one sees throughout history. My impression is that Our Lady wanted to give ordinary people, who might not know how to pray, this simple method of getting closer to God."  Sister Lucia, one of the seers of Fatima.