I appreciate your desire for the truth Mark. Experimental evidence, though, is not the only kind of valid evidence (Can you prove that it is or is not by through experiment?).

Those who believe in prayer can often witness to a far more powerful type of evidence - experiential evidence. You cannot argue with those who have experienced the power of prayer. 

Paradoxically, you also cannot know the power of prayer unless you try it.
Try it and see what happens. What can it hurt? Just be open minded about the results and perhaps you will be surprised.

Peace!