Answer
I have heard conflicting accounts of Calvin's ordination in the Roman Catholic Church, but to my mind his lack of ordination in a Protestant church is good evidence that he was ordained as a Catholic. There would be no need for re-ordination in a Protestant church, since both the Roman Catholic and the Protestant churches are part of the same visible church (per Reformed/Protestant doctrine). Of course, there are no Roman Catholic ordinations into the Protestant church. The Roman Catholics did not recognize the legitimacy of the Protestant churches. And at any rate, it is not the practice of any church body to ordain members into other church bodies.
The main point I was trying to make was that the Bible does not teach that we need to be able to draw a dotted line of succession back to Christ. For example, Scripture nowhere teaches that it is invalid for a few Christians to start their own church and ordain their own ministers. Jesus teaching in Mark 9:38-40 is instructive in this regard. There he taught that anyone who is faithful to him can minister in his name, and thereby with his authority, even if they don't have a connection to the apostles. Notice that in this case the authority of the man was proven not only by Christ's words, but also by the Holy Spirit who empowered the man to exorcise demons.
In fact, it is God's standard practice throughout Scripture to call servants from outside his established formal orders when the established formal orders fall into sin or apostasy. For example, he regularly called prophets who had no connection to other prophets, or to the king, or to the priesthood. He replaced wicked kings with others who were not from their bloodline. He called foreign nations to judge his people. He replaced the leadership of Israel with Christ. He abandoned Israel as the covenant community that contained the faithful remnant, and reconstituted that covenant community around Christ. These facts demonstrate that just like our inheritance is traced spiritually and not physically, succession is spiritual matter and not a physical one (cf. Abraham's fatherhood over the faithful in Rom. 4).
Moreover, the Bible demonstrates time and again that the groups that have clear lines of physical succession can be apostate. The greatest example of this in Scripture is the division between Christ and Israel. Christ was not part of the tribe of Levi, he was excommunicated and sent to his death by the Jewish religious institution, but he nonetheless is our legitimate high priest and the heart of the faithful remnant of God's people. Moreover, even in the Bible, churches started by apostles were subject to apostasy (cf. Paul's letter to the Galatians, and Christ's letters to the churches in Revelation). And in the post-apostolic age, the entire church abandoned Trinitarianism in the time of Athanasius, so that Trinitarians were considered heretics, and Athanasius was exiled repeatedly. Even today the "gospel" preached by the Roman Catholic Church is not the gospel of Scripture.
Given the choice between a church with apostolic succession and a false gospel, or a church without succession but with a true gospel, the biblical solutions seems clear to me: choose the church with the true gospel.
In summary, the items you mentioned as concerns are not concerns in Scripture (e.g., tracing back through Christ in an unbroken line of succession, sectarianism), and the requirements you believe to be important are not requirements in Scripture (e.g., unbroken line of succession). The Roman teachings may make sense from a human standpoint, but they are contrary to the Bible. Yes, there is some wisdom in following the established church — as our "ordinary" practice. But in order to be true to Scripture, we must also allow for "extraordinary" practices, especially when the "ordinary" means fail to fulfill their duty to God. This is what happened throughout the Old Testament, it is what happened in the days of Christ, it is how the early church was separated from Judaism, and it is what happened in the Reformation. In cases like this, to reject God's extraordinary means is reject his plan and purpose.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.