How does one menstruate with a blocked fallopian tube?

Hormones by blood: An open fallopian tube is only needed for the egg to pass through. As the egg is developing in the ovary it produces hormones - estrogen and then Progesterone after ovulation. These hormones go through the bloodstream to reach the uterus and cause the lining to grow and shed in a cyclic fashion. The egg still ovulates but just gets resorbed in the abdomen.