What is the Catholic Church's position of a marriage between a menopausal woman and an impotent man? Since the purpose of marriage in Catholicism is for procreation, what is the position of the Catholic Church of a man and a woman being married for the first time when the woman is past childbearing age and the man is impotent because of his age? (The marriage cannot be consummated.)
This one is easy: impotence makes marriage impossible (invalid). To quote the Code of Canon Law,


  Can.  1084 §1. Antecedent [i.e, before the marriage consent is given] and perpetual [i.e., permanent] impotence to have intercourse, whether on the part of the man or the woman, whether absolute [i.e., the person is incapable of intercourse with anyone at all] or relative [i.e., the person is incapable of intercourse specifically with his perspective spouse], nullifies marriage by its very nature.


In this case, the reason does not have to do so much with procreation, as with the fact that marriage by its very nature entails at least the possibility of engaging in sexual intercourse. That is, evidently, not possible in the case of impotence, and so neither is marriage.

Therefore, the mere fact that the woman is past childbearing age is not an impediment to marriage—the problem in the case described by the O.P. would be entirely with the man’s impotence.

It should be noted that impotence here is defined as the inability to engage in the sexual act. It is distinct from infertility or sterility, which is the inability to father or conceive children.

The Code of Canon Law specifies that infertility (as opposed to impotence) is not an impediment to marriage. From the same canon:


  §3. Sterility neither prohibits nor nullifies marriage, without prejudice to the prescript of can. 1098. [Can. 1098 essentially says that if important problems such as infertility are concealed from a prospective spouse, that could be grounds for invalidity. However, it is not the infertility as such that renders the marriage invalid.]


It should also be specified that this impediment holds for new marriages (which is why Canon Law specifies that only antecedent impotence can impede marriage). Impotence acquired after the exchange of consent does not affect validity.