bnorton, I do not think that this is a valid example since Diana was dead by the time we heard about the accident. Also, I think a lesson could’ve been learned by comparing public reaction of her death to the reaction of Mother Teresa’s death which was only a few days later. The words you heard describing Diana, such as honorable, good, postive, loving, etc., can, I hope no one argues this, also be attributed to MT perhaps even more dramatically. Yet no one seemed to care when MT died. To me it proved that the world is more amazed by glamour and prestige than by someone who devotes her entire life to a cause.
Pretty clever, I’ll acknowledge. 
And now to face my executioners about faith and prayer. I have heard an explanation of faith that I will pass on. There are three types of faith: natural, rational, and experiential. All humans, primitive and civilized, have in them a natural faith, instilled by God, which compels them to believe in a higher power (though not neccessarily God). This faith gives them a sense of right and wrong and a feeling of weakness and vulnerability (to nature, other men, etc.). Primitive men thus started worshipping the sun, the moon, the sea. Civilized man, however, did not pursue these natural objects as gods but started developing philosophy and science and other things to bring comfort to themselves. Although the paths were different, the goal was to appease the same built-in consience we all have. As J.P. Sartre complained, “Man is a useless lost hope.”
Rational faith is when we try to assimilate the divine revelations and tenets of natural faith. It is an attempt to understand what cannot be comprehended by reason alone. But this type of faith tries to simplify the truth, thus distorting it, and does not accept that we are in over our heads when we try to understand the world by ourselves.
Experiential faith is the faith that takes a stand. Faith “is the gift of God” (Eph. 2:8) and is what keep you with God when the going gets tough and allows you to turn back to God when you become enslaved in sin. This faith is given to you when you accept the fact that you are a sinner, vulnerable, and hopeless without God. You must turn to God (through Christ) to receive this faith. You cannot just give it lip service, you must truly be willing to accept the truth. You then start seeing some amazing things in your life. You feel secure and peacable, confident that you are on the path to salvation (thus getting rid of that nagging fear of death all humans have), you feel more love in your life and are able to find good when ther only seems to be evil. Most importantly, as you read the Scripture, pray, and start trying to lead your life the way it is commanded your relationship with God grows and more is revealed to you.
Does prayer work? Yes, when it is part of an active faith process and when you ask for the right things. Is there proof? Only from the testimony of those who say it has worked. Remember that the only thing you can truly “prove” in this world, if you look at it scientifically, is that you exist. You cannot prove anything else. I believe as many others do that when you turn to God with humility and sincerity through prayer and through the Scripture you will be richly rewarded.