As I read your letter, I couldn't help but wonder if you've ever faced a serious health crisis, either in your own life or in the life of someone you love. When people do, I find, they almost always turn to prayer -- even if they haven't had much to do with God.
Why is this? One reason, I believe, is because we all know that even with the best medical care, things can go wrong, and healing is not assured. In addition, some situations are so serious that there seems to be little or no hope of recovery. We also know that our bodies and our minds are very closely connected, and if a person is very discouraged or doesn't want to live, their recovery is doubtful. Why shouldn't we pray for them?
Your question, however, suggests to me that the real reason for your letter is that you simply don't believe God answers prayer, or that He cares for us. You may not even believe He exists, or at least you're uncertain about it.
Whatever your reasons, I challenge you to examine your doubts in the light of Jesus Christ. He was God in human form, and He came into the world to bridge the gap between us and God. Don't let doubt keep you in its grip any longer, but open your heart and mind to the truth found in Jesus Christ. He alone could say, "I am the way and the truth and the life" (John 14:6).