Which other hormone is not produced if there is no menstrual cycle?

Not a clear question: Estrogen and progestrone are the two main hormones associated with the cycle. But it is the amount of sectretion (surge or up-and-down) that makes a difference. When ovaries are active, at the time of egg release there are certain amount of secretion of each above hormones that set the stage. So when there is no cycle (due to menopause, etc), the levels of few hormones can be affected.

Progesterone : Is produced during ovulation. Estradiol is produced by the follicle. During perimenopause often a follicle will develop and produce estradiol but never ovulate to produce progesterone. There can be bleeding during this transition but it is not cyclic. After all eggs are exhausted ( menopause) there is no bleeding.