I guess I'm a little confused over what the OP means when it uses the term "regenerated," i.e., "born again" and the way JamesL uses it.
"Regeneration" in the New Testament simply means "born again," and while we usually have someone make the statement "'Born Again' in John 3 simply means
born from above," and that is true, it also remains true that when one is born again it is a given that they are born from above, or, as we see in many places, Born of God:
John 1:12-13
King James Version (KJV)
12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
13 Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
Here we see that receiving Christ (which is contrasted with "receiving Him not," which is rejection) makes it possible for men to be made sons of God, that is accomplished by believing on His Name, and the result is they are born of God at that time.
Here...
1 John 5:1-5
King James Version (KJV)
1 Whosoever believeth that Jesus is the Christ is born of God: and every one that loveth him that begat loveth him also that is begotten of him.
2 By this we know that we love the children of God, when we love God, and keep his commandments.
3 For this is the love of God, that we keep his commandments: and his commandments are not grievous.
4 For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith.
5 Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?
...we see again faith and belief in Christ is the means of overcoming, which is synonymous with salvation. To overcome means one has had faith in Christ, and is born of God.
"Overcoming" is through faith in Christ, and that...alone.
Now we will look at another statement concerning New Birth:
James 1:18
King James Version (KJV)
18 Of his own will begat he us with the word of truth, that we should be a kind of firstfruits of his creatures.
This reiterates John's statement in his Gospel that we are born of God according to His will, not of blood (natural birth, or natural disposition), not of the will of the flesh (we cannot effect regeneration through any natural effort on our part), and not of the will of man.
This last "will" speaks of God's intervention on behalf of fallen man, and it is a basic pattern for all who have ever been declared just that God first intervenes through revealing Himself and His will to men, then they are saved.
1 Peter 1:18-23
King James Version (KJV)
18 Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers;
19 But with the precious blood of Christ, as of a lamb without blemish and without spot:
Hebrews 9 (as was pointed out by JamesL) teaches about eternal redemption through Christ's blood (death). While the Old Testament Saint received atonement through the prescribed method God allowed (vicarious death, and animals dying instead of the sinner), that atonement was temporary and temporal, which is why the Writer points out they were offered continually...for the same sins.
But we, as well as the Old Testament Saints, have been eternally redeemed through the Atonement provided in and through Christ.
20 Who verily was foreordained before the foundation of the world, but was manifest in these last times for you,
Removes all controversy as to whether the "Blood was applied" prior to His death. The Old Testament Saint was declared just, but, had to be made perfect (complete) by the Sacrifice of Christ, contrasted many times with the temporary provision of the Law and the sacrifices that preceded the Law.
21 Who by him do believe in God, that raised him up from the dead, and gave him glory; that your faith and hope might be in God.
22 Seeing ye have purified your souls in obeying the truth through the Spirit unto unfeigned love of the brethren, see that ye love one another with a pure heart fervently:
23 Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever.
The "Word" in view is the Gospel of Christ. That is how we are saved. That is how one is born again. Not one Old Testament Saint can be said to have trusted in Christ's death (required according to Christ in John 6), though He was prophesied. Again, the expectation in Christ was carnal, because that was how they understood the revelation provided them.
And key to regeneration is the Baptism with the Holy Ghost, for salvation in Christ is made complete in regards to sin and reconciliation.
Consider:
Titus 3:4-5
King James Version (KJV)
4 But after that the kindness and love of God our Saviour toward man appeared,
5 Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;
We are saved by...
...the washing of regeneration, which speaks of the promised cleansing which takes place when one is made a "new creature," which itself effected by...
...the renewing of the Holy Ghost, which is the "reunion" of God with man. Rather than the Holy Ghost renewing us, which is already pointed out in the washing of regeneration.
Man was separated from God through Adam's sin, and the means of reunion of God and man is Christ our Lord and the Work on the Cross. That union which was lost in Adam is restored, renewed in salvation according to New Covennat standard.
Granted, prior to the cross & resurrection, the people who received their regeneration were, in a sense, not "fully regenerated" since Christ's death and resurrection hadn't taken place yet, OTOH they were still "believers" because they were trusting in the finished work of Christ--even though His finished work was still something that would occur in the near future.
Scripture does not teach a partial "new birth." While men effect "partial births," and we can see the abomination that is, God does not recreate men partially, but completely.
We are made new creatures, and what is taking place is a spiritual resurrection, which as Christ taught, is like the wind: we can see the effect, but not what effects that affect.
But you are correct in saying they were believers, but, keep in mind that they believed only the revelation they had at that time. Probably most in Israel in Christ's Day longed for Christ, and were aware of the prophecy, but, that expectation was limited by the fact that the Gospel of Christ was not yet revealed to them.
Anyway, they were still believers in Christ as opposed to those who never believed in Christ, and, as such, IMHO, they would have been "born again."
Consider the passages provided, and give them some thought. I view this as one of the most important issues we will ever consider, and we owe it to the Lord to do our due diligence in regards to it.
The Lord questions the "belief" of the disciples here...
John 16:28-32
King James Version (KJV)
28 I came forth from the Father, and am come into the world: again, I leave the world, and go to the Father.
29 His disciples said unto him, Lo, now speakest thou plainly, and speakest no proverb.
30 Now are we sure that thou knowest all things, and needest not that any man should ask thee: by this we believe that thou camest forth from God.
31 Jesus answered them, Do ye now believe?
32 Behold, the hour cometh, yea, is now come, that ye shall be scattered, every man to his own, and shall leave me alone: and yet I am not alone, because the Father is with me.
Their "belief" was not enough for them to maintain loyalty to the Lord, but they to the man abandoned Him.
We do not negate the fact that they were "saved" according to Old Testament standard, and their salvation as secure as any born again believer post-Cross, but, that does not disannul their need for eternal redemption through Christ, nor grant them a spiritual, rather than natural state. These men were not eternally indwelt, though the Spirit of God ministered to them:
John 14:16-17
King James Version (KJV)
16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;
17 Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
Understanding the distinction between ministries of God and the progressive nature of revelation and the unfolding of the Redemptive Plan through that progression will unlock what many see to be inconsistencies in Scripture. It will help balance the Word of God as we begin to see that Salvation through Christ is not Plan B, but God's intention from before the world was formed:
Romans 16:24-26
King James Version (KJV)
24 The grace of our Lord Jesus Christ be with you all. Amen.
25 Now to him that is of power to stablish you according to my gospel, and the preaching of Jesus Christ, according to the revelation of the mystery, which was kept secret since the world began,
26 But now is made manifest, and by the scriptures of the prophets, according to the commandment of the everlasting God, made known to all nations for the obedience of faith:
God bless.