Prayer absolutely can work, which is why enlightened leaders such as the current Dalai Lama discourage conversion. For millions or billions of people, the precise things they believe matter less in reality than that they believe, and have learned through prayer, meditation, or whatever form of focused, accepting intention they have learned to utilize, to affect the subtle aspects of themselves and through that their world.
I would not have survived my early years without faith (lowercase) and many miracles occurred through prayerful focused intention.
I am a rare one who needed to change belief systems completely, but I follow the same star.
Remembering what it felt like within me when I was a frightened pre-teen left alone with a feverish and miserably sick little sister and how afraid a and full of hurt for her, I knelt and prayed and felt a wash of love and comfort, and felt the sickness dissipate and be replaced with healthy sleep, years later I can feel the same accepting love and hold the same intention and heal others with the same calm assurance I had at twelve. All faiths, including non-faith, that are effective, draw on the same truths and same power for good, call Him, Her, They, it, or us what you may.