What is the religious ruling on helping my elderly father (73 years old) get married again, taking into account that he previously backed out of marriage due to his physical inability, and is it obligatory for me to marry him off despite my fear that he will refuse again for the same reason?

Indeed, marrying off a father who is unable to afford the dowry and is in need of chastity is one of his obligatory rights upon his affluent children. His request in this regard must be fulfilled. His previous refusal to marry does not justify rejecting his request now, as he might have had temporary reasons that have since disappeared. His advanced age does not preclude his desire for and ability to marry and engage in marital relations.