Didn’t Moroni mean to say that they ordained them by the power of the priesthood? No, he did not. Of course, they were ordained by the power of the priesthood, but there is a relationship between priesthood and the Holy Ghost that we sometimes don’t fully understand.
“Without the Holy Ghost there can be no revelation, and without revelation there can be no priesthood, for the priesthood is the authority to speak for God. Having discussed the various orders of the priesthood, the Prophet said: ‘The Holy Ghost is God’s messenger to administer in all those priesthoods’ (Teachings, p. 323). Thus we find Moroni saying, ’And after this manner did they ordain priests and teachers, according to the gifts and callings of God unto men; and they ordained them by the power of the Holy Ghost, which was in them’ (Moroni 3:4). Similarly, the revelation that lays the foundation of the government of the Church in this dispensation states: ’Every elder, priest, teacher, or deacon is to be ordained according to the gifts and callings of God unto him; and he is to be ordained by the power of the Holy Ghost, which is in the one who ordains him’ (D&C 20:60)…Having said that without the Holy Ghost there can be no priesthood, let us now say, conversely, that without the priesthood there can be no gift of the Holy Ghost.” (Millet & McConkie, Joseph Smith: The Choice Seer, chap. 5, “The Priesthood and the Holy Ghost”)
"How is the Holy Ghost Involved in Ordinations? A man may properly wire his house for electricity, observing the code most carefully. Still, if the power company refuses to connect him to the power source, no lights or heat will come on in his house. He could turn switches to no avail…The Prophet Joseph Smith said the following:
’We believe in the gift of the Holy Ghost being enjoyed now, as much as it was in the Apostles’ days; we believe that it is necessary to make and to organize the Priesthood, that no man can be called to fill any office in the ministry without it; we also believe in prophecy, in tongues, in visions, and in revelations, in gifts, and in healings; and that these things cannot be enjoyed without the gift of the Holy Ghost.’ (Teachings of the Prophet Joseph Smith, p. 243)
"Elder James E. Talmage illustrates the sustaining influence of the Holy Ghost in the callings and operations of the priesthood:
’Ordination of Men to the Ministry, as sanctioned by scriptural precedent and established by direct revelation of God’s will, is to be effected through the gift of prophecy and by the impositions of hands by those who are in authority. By prophecy is meant the right to receive and the power to interpret manifestations of the divine will.’ (Articles of Faith, p. 182)" (Book of Mormon Student Manual, 1981, p. 508)
Evidence that the Aaronic Priesthood was not had among the Nephites, even after the visitation of Christ:
Evidence that the Aaronic Priesthood was had among the Nephites after the visitation of Christ:
Joseph Fielding Smith said so: “When the Savior came to the Nephites, he established the Church in its fulness among them, and he informed them that former things had passed away, for they were all fulfilled in him. He gave the Nephites all the authority of the priesthood which we exercise today. Therefore we are justified in the belief that not only was the fulness of the Melchizedek Priesthood conferred, but also the Aaronic, just as we have it in the Church today; and this Aaronic Priesthood remained with them from this time until, through wickedness, all priesthood ceased. We may be assured that in the days of Moroni the Nephites did ordain teachers and priests in the Aaronic Priesthood; but before the visit of the Savior they officiated in the Melchizedek Priesthood.” (Answers to Gospel Questions, 1:124-26.)