Yes, prayer does work. Our son, Thomas, was very sick about 5 years ago from e. coli. The doctor said all of the literature said that in his advanced state of sickness (kidney shutdown, pancreatic bleeding, etc.), he was as good as gone (not the doctor's exact words). We had several churches praying for Thomas, and after 30 days he came home from the hospital and now is an active 9 year old with 50% kidney function, which should be adequate if maintained.
So, my faith was reaffirmed, and whenever somebody asks for prayers, I happily oblige, because somebody is listening! Best of luck and God bless.