How do you know that Noah and the others did not have the Spirit of God.
Well, the Bible says that "the Spirit was upon" so-and-so, if he was. Simeon, who prophesied over the infant Jesus. is an example of this:
Luke 2:25
25 And there was a man in Jerusalem whose name was Simeon; and this man was righteous and devout, looking for the consolation of Israel; and the Holy Spirit was upon him.
(See also: Balaam - Numbers 24:2, Gideon - Judges 6:34, Jephthah - Judges 11:29, Samuel - 1 Samuel 10:10, etc.)
Prior to the Atonement of Christ at Calvary, the Spirit came and went from people, not indwelling them permanently, as he does now, post-Calvary. In any case, it isn't ever said of Job that the Spirit was upon him. Nor is this ever said of Noah, either, though God spoke to him at various times. Before his conversion, Cornelius also, is never said in Scripture to have had the Spirit upon him, though he did have a vision in which he was instructed by an angel to visit Peter.
I know that it is the general teaching of Calvinism that you have to be regenerated or born again, but I'm not sure.
It is one of the...peculiarities of Calvinism that it holds that a person must first be born-again (spiritually regenerated) in order to understand and believe the Gospel (which is what Scripture says is necessary to being born-again). I don't know that every professing Calvinist would say this, but certainly the harder-line Calvinists, like R.C. Sproul, held to this ordo salutis, bizarre though it is.
Romans 10:13-14
13 For “everyone who calls on the name of the Lord will be saved.”
14 How then will they call on him in whom they have not believed? And how are they to believe in him of whom they have never heard? And how are they to hear without someone preaching?
Romans 1:16
16 For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek.
John 20:31
31 but these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name.
As these verses plainly indicate, the Bible's ordo salutis is that believing in Jesus necessarily precedes salvation (which is synonymous with spiritual regeneration). Nowhere in the Bible have I ever read that the Spirit must first spiritually regenerate a person so that they then can believe and be saved. The doctrinal contortions of Calvinism, however, demand this inversion of the actual order of things.
The Arminians who were against Calvinism but still had to admit in man's total depravity came up with a work around called "Prevenient Grace." This is a pre-conversion work of the Holy Spirit that makes a person able to come to Christ, but is still resistible. They believed it is given to everybody. That is why it had to be resistible or everybody would be saved.
They "came up" with the doctrine of prevenient grace as a "work around"? That's not what Arminians would say. Instead, they would point to Scripture that amply establishes their view. John 16:8, John 6:44 and 2 Timothy 2:25 all indicate that God must act to convict, illuminate and enable a change of mind about the Gospel in the mind of a lost person. But as Romans 1:16 says, the "power of God for salvation" resides in the truth of the Gospel itself though it is contingent in its salvific effect upon the lost person choosing to believe the Gospel. Jesus himself illustrated this in his mournful words to the city of Jerusalem:
Luke 13:33-34
33 "Nevertheless I must journey on today and tomorrow and the next day; for it cannot be that a prophet would perish outside of Jerusalem.
34 "O Jerusalem, Jerusalem, the city that kills the prophets and stones those sent to her! How often I wanted to gather your children together, just as a hen gathers her brood under her wings, and you would not have it!
There is nothing of the compulsive here in what Jesus says. Instead, his desire for the children of Jerusalem is subjected to their choice to reject him - just as happens with the Gospel. This isn't a "work around" but what is quite evident in Scripture.
I kind of believe in something like that, but it is only given to those God has chosen and it is irresistible. Thus Noah and all those you mentioned.
But you're making an unwarranted assumption, here, about Noah, Job and Cornelius. See above.