As malphono stated,
If there are no impediments, Transubstantiation still occurs.
*]Proper minister of the Sacrament (the properly ordained ministerial Priest)
*]Proper intent by the minister (intending what the Church intends)
*]Proper form (in this case one of the Eucharistic Prayers)
*]Proper matter (the Priest cannot “Consecrate” oatmeal for example)
Berengarius learned this first hand.
When you asked:
I don't just mean doubt, I mean active disbelief.
The Consecration still occurs.
In my answer I meant to apply this possibility and 1st Corinthians 11:27-34 to a Priest saying the Mass alone. Sorry. I guess I wasn't clear on this.
1st CORINTHIANS 11:29 29 For any one who eats and drinks without discerning the body eats and drinks judgment upon himself.
This is true for “any one”, not just the congregation but even the Priest. If there were no real consecration, he wouldn't be guilty of such a profanation (elsewhere in the pericope, it even talks being "guilty of profaning the body and blood of the Lord").
You also said,
Anyone can baptize. One does not have to be ordained to baptize and the person baptizing does not have to believe in it. For me, this raises the question why does one have to be ordained to consecrate the gifts? What is the significance of ordination in consecrating the gifts?
Differing functions of clergy and laity for more effective evangelization of the world.
Clergy Holy Orders is directed at is at the service of the common priesthood (It is for the service of us) and for their fellow clergy.
Laity Our non-ministerial Priesthood that we have (when we are Baptized) is the common priesthood of the faithful and is exercised by the unfolding of baptismal grace --a life of faith, hope, and charity, a life according to the Spirit to be sent out into the world to sanctify it in a sense by bringing Christ to the world.
The Holy Sacrifice of the Mass empowers us to do this. "The Mass has ended. Let us go in peace to love and serve the Lord. . . .Thanks be to God!"
CCC 1536 Holy Orders is the sacrament through which the mission entrusted by Christ to his apostles continues to be exercised in the Church until the end of time: thus it is the sacrament of apostolic ministry. It includes three degrees: episcopate, presbyterate, and diaconate.
Excerpt from CCC 1538 . . . . Today the word "ordination" is reserved for the sacramental act which integrates a man into the order of bishops, presbyters, or deacons, and . . . it confers a gift of the Holy Spirit that permits the exercise of a "sacred power" (sacra potestas)5 which can come only from Christ himself through his Church. Ordination is also called consecratio, for it is a setting apart and an investiture by Christ himself for his Church. . . . .
CCC 1547 The ministerial or hierarchical priesthood of bishops and priests, and the common priesthood of all the faithful participate, "each in its own proper way, in the one priesthood of Christ." While being "ordered one to another," they differ essentially.22 In what sense? While the common priesthood of the faithful is exercised by the unfolding of baptismal grace --a life of faith, hope, and charity, a life according to the Spirit--, the ministerial priesthood is at the service of the common priesthood. It is directed at the unfolding of the baptismal grace of all Christians. The ministerial priesthood is a means by which Christ unceasingly builds up and leads his Church. For this reason it is transmitted by its own sacrament, the sacrament of Holy Orders.
VATICAN II LUMEN GENTIUM (excerpt from sections 18, 31-32) 18. For the nurturing and constant growth of the People of God, Christ the Lord instituted in His Church a variety of ministries, which work for the good of the whole body. For those ministers, who are endowed with sacred power, serve their brethren, so that all who are of the People of God, and therefore enjoy a true Christian dignity, working toward a common goal freely and in an orderly way, may arrive at salvation. . . . .31b But the laity, by their very vocation, seek the kingdom of God by engaging in temporal affairs and by ordering them according to the plan of God. They live in the world, that is, in each and in all of the secular professions and occupations. They live in the ordinary circumstances of family and social life, from which the very web of their existence is woven. They are called there by God that by exercising their proper function and led by the spirit of the Gospel they may work for the sanctification of the world from within as a leaven. In this way they may make Christ known to others, especially by the testimony of a life resplendent in faith, hope and charity. Therefore, since they are tightly bound up in all types of temporal affairs it is their special task to order and to throw light upon these affairs in such a way that they may come into being and then continually increase according to Christ to the praise of the Creator and the Redeemer.
32. By divine institution Holy Church is ordered and governed with a wonderful diversity. "For just as in one body we have many members, yet all the members have not the same function, so we, the many, are one body in Christ, but severally members one of another". . . .
For more details see section 18-38 here.
I hope this helps minkymurph.