How strong of a dispensationalist are you? For example, Do you believe that salvation is different during different times? Do you believe that there is no connection between the new covenant and the new birth?

I am very dispensational, though probably more in the classical sense (Chafer, Scofield, etc.). However, the "strong" dispensationalism that is now coming out of certain King James Bible camps is stronger than I can accept for myself. I do accept that the route to salvation from the human side changes from dispensation to dispensation. However, I have come to the conclusion that there are three foundations of salvation that are fundamental and universal to every dispensation. They are:

1. The blood of Christ must be applied to every soul that goes to heaven. The difference is that the OT saints had to wait on that application until after their death while we have the blood applied immediately at the time we believe. However, I have yet to see any reason for believing that any future dispensation will not have the immediate application of His blood. That would be retroactive and makes no sense to me.
2. The faith of man is required for salvation in every dispensation. I do believe that the content of that faith changes dispensationally. I also believe that the distinction between faith and works may not be as clear in every dispensation. For instance, in the kingdom age, the faith will be much more consistently displayed in the works of the believer than it is today. Yet, man must always believe.
3. The grace of God is the only way by which a man may go to heaven. Dispensationally, this grace may not be as obvious in every dispensation. I have no qualms in calling this the age of grace. But ultimately, all are saved because of the grace of God--because God gave them the undeserved gift of eternal life.

Now, because of my approach, I have come to reject two of the tenets of the strong dispensationalists (I reserve "hyper" for those who reject water baptism). As such, I reject:

1. Salvation by faith AND works in any dispensation. I am convinced that the Bible clearly teaches that these two things cannot share in being the cause of salvation. For one thing, faith and grace work hand in hand (Romans 4:16Therefore it is of faith, that it might be by grace; to the end the promise might be sure to all the seed; not to that only which is of the law, but to that also which is of the faith of Abraham; who is the father of us all,
   See All...; Ephesians 2:8For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
   See All...), but grace and works are not compatible (Romans 11:6And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then it is no more grace: otherwise work is no more work.
   See All...). Therefore, faith and works are not compatible either--not as mutual causes of salvation.
2. Limiting Hebrews through Jude to the doctrine of the tribulation age. I go so far as to accept that a couple of these books have some powerful applications to the tribulation (especially James). But they were written to Christian believers (though mostly Jewish believers) during the time of the age of grace. I believe that to make their doctrine non-Christian denies their clear and immediate first purpose. In fact, one of the three times the word "Christian" is used in the Bible is in this section: 1 Peter 4:16Yet if any man suffer as a Christian, let him not be ashamed; but let him glorify God on this behalf.
   See All....

As you can see in my post, Regeneration in the Old Testament, I am not ready to declare regeneration as an absolute doctrine for earlier dispensations. However, I do recognize some form of salvation experience. Else, how could they come to know the Lord (as in 1 Samuel 3:7Now Samuel did not yet know the LORD, neither was the word of the LORD yet revealed unto him.
See All...) or come to be "in faith" (as in Hebrews 11:13These all died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth.
See All...)?

You mention that the New Covenant and the new birth could have nothing in common because the New Covenant was not for the Gentiles. I agree that the New Covenant is a Jewish Covenant. However, when Jesus introduced the new birth to Nicodemus in John three, could He not have been dealing with the coming of the New Covenant to Israel? Israel had not yet rejected Jesus as their Messiah. If they had accepted Him, He would have quickly (seeing that a few years is much quicker than 2000) moved toward establishing the kingdom and the New Covenant. I still believe that Christ may have expected Nicodemus to have known about the new birth by way of New Covenant teaching.

You mention a possible connection between the New Testament and the New Covenant. The second is based on the first. I agree and teach this as well. I conclude that through the New Testament those of us in the age of grace have been able to enjoy some of the blessings of the New Covenant even though it is not our covenant and it has not yet fulfilled the purpose for which it was originally promised. The New Covenant is embodied in the coming of Christ and we have the blessings of Christ, even though the New Covenant does not technically apply to us.

We know also that the new birth was not an exclusive benefit of the Jews under the New Covenant. Too many grace age passages refer to the new birth in various phrases. We are "born after the Spirit" (Galatians 4:29But as then he that was born after the flesh persecuted him that was born after the Spirit, even so it is now.
See All...), "begotten...through the gospel" (1Corinthians 4:15For though ye have ten thousand instructers in Christ, yet have ye not many fathers: for in Christ Jesus I have begotten you through the gospel.
See All...), and regenerated (Titus 3:5Not 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;
See All...).