The "new heart" and "new mind"
and the "new spirit," for that matter, are the result of being immersed into God in eternal union, or in other words, we are born again and are therefore "new creatures" as a result of being indwelt by God.
The OP was looking more at the ability/inability of the natural man to have faith. Its a centuries old debate, one side saying natural man can hear the Gospel, understand, and place saving faith in Christ, the other side saying "No, natural man cannot understand the spiritual things of God, so God must regenerate men so they can have saving faith."
Both are wrong, in my view, and I have presented my view in the preceding posts. The Comforter ministers to natural men/women and enlightens their minds to the truth of the Gospel, and men respond, either receiving the truth or rejecting. That does not mean that they are made regenerate during this ministry. And I think if most of us look back we can see that the process of our own conversions were not instantaneous, but there was a period where we came under conviction until that day we acknowledged the truth and pleaded (in my own case) with God to forgive us and save us.
No, only those who die during the Tribulation are glorified when Christ returns. There is a difference between the Rapture taught by Paul, where the entire Church is resurrected physically (first the dead in Christ and then we which remain alive, 1 Thessalonians 4:13-18), and the Second Coming of Christ (Revelation 19). When Christ returns He will destroy the unbelieving from among the population (the Sheep and Goat judgment, Matthew 25), and those who are believing, who were born again during the Tribulation, are those who enter into the Millennial Kingdom that Christ establishes when He returns. I think we see in Daniel 12 a 75 day period where this establishment of the Kingdom takes place. Satan is bound for one thousand years when Christ Returns, and this at the time He returns, which gives roughly 75 days at the end of the Millennial Kingdom for Satan to once again gather unbelievers under him. These unbelievers will be destroyed, along with Satan, and at that point God causes this Creation to pass out of existence, the Great White Throne Judgment takes place, and the new heavens and Earth are created (Revelation 20-21).
So those alive at the Second Coming will be physical, born again believers, who enter the Kingdom promised to Israel, though for the benefit of all families of the earth.
This speaks of the physical destruction of unbelievers when Christ returns...
Luke 17:24-37
King James Version (KJV)
24 For as the lightning, that lighteneth out of the one part under heaven, shineth unto the other part under heaven; so shall also the Son of man be in his day.
25 But first must he suffer many things, and be rejected of this generation.
The context deals with the Second Coming.
The next passage defines what is going to happen, and we see it is a matter of physical judgment, for those are the examples it is said to be like:
26 And as it was in the days of Noe, so shall it be also in the days of the Son of man.
27 They did eat, they drank, they married wives, they were given in marriage, until the day that Noah entered into the ark, and the flood came, and destroyed them all.
28 Likewise also as it was in the days of Lot; they did eat, they drank, they bought, they sold, they planted, they builded;
29 But the same day that Lot went out of Sodom it rained fire and brimstone from heaven, and destroyed them all.
30 Even thus shall it be in the day when the Son of man is revealed.
31 In that day, he which shall be upon the housetop, and his stuff in the house, let him not come down to take it away: and he that is in the field, let him likewise not return back.
32 Remember Lot's wife.
Just as in the days of Noah and Lot unbelievers were destroyed physically, even so when the Son of Man returns, so too will the unbelievers be destroyed.
The next passage is a statement of specificity as to the fate of the unbelievers:
33 Whosoever shall seek to save his life shall lose it; and whosoever shall lose his life shall preserve it.
34 I tell you, in that night there shall be two men in one bed; the one shall be taken, and the other shall be left.
35 Two women shall be grinding together; the one shall be taken, and the other left.
36 Two men shall be in the field; the one shall be taken, and the other left.
37 And they answered and said unto him, Where, Lord? And he said unto them, Wheresoever the body is, thither will the eagles be gathered together.
The "eagles" are carrion fowl. When Christ makes this same statement as recorded by Matthew we see...
Matthew 24:27-28
King James Version (KJV)
27 For as the lightning cometh out of the east, and shineth even unto the west; so shall also the coming of the Son of man be.
28 For wheresoever the carcase is, there will the eagles be gathered together.
Again, this is a separate event from the Rapture, and again, only the Tribulation Martyrs are glorified when Christ returns:
Revelation 20:4-6
King James Version (KJV)
4 And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years.
5 But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection.
6 Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.
And I will throw in that the "first" in First Resurrection is protos, and can mean both first in a sequential context, but here means "first" in a context of rank. There are only two resurrections taught in Scripture, the resurrection unto life, and the resurrection unto damnation. That is the context of first here, because we know it is not the first in sequence, seeing we have First the Resurrection of Jesus Christ, the Firstborn from the dead, then we have the Rapture, then we have the Two Witnesses (Revelation 11), then we have the resurrection of the Tribulation Martyrs.
God bless.