Joseph: Thanks for your comments. I do understand that these two expressions are interchangeable. Since Matthew was writing to a primarily Jewish audience he would have used the phrase "Kingdom of heaven" out of respect for the Jews who did not write out the word God. Considering this, it would be incorrect to draw the conclusion that the OT faithful have a heavenly destination from these two scriptures alone. However, when considered in combination with Hebrews which refers to a heavenly city prepared for them, it would seem to make sense that the OT men could have a heavenly hope.
Having said that, my argument of the OT faithful having a heavenly hope does assume that you actually believe in a heavenly resurrection, which I can see by your comments you do not. I would like to address the two scriptures you cite to support your belief:
You mention that the only one qualified to go to heaven was Jesus as he was from there and since we are human (born of flesh) we do not qualify. I would agree with this reasoning. However, reading the entire chapter of John 3 in context, wasn't the whole purpose of Jesus' discussion with Nicodemus to demonstrate that (as you say) no one born of flesh (man) can enter the Kingdom of God, so therefore we must be born again of Spirit to do so...
John 3: 3 In reply Jesus declared, "I tell you the truth, no one can see the kingdom of God unless he is born again."
4"How can a man be born when he is old?" Nicodemus asked. "Surely he cannot enter a second time into his mother's womb to be born!" 5Jesus answered, "I tell you the truth, no one can enter the kingdom of God unless he is born of water and the Spirit. 6Flesh gives birth to flesh, but the Spirit gives birth to spirit.
Applying this same line of reasoning that flesh (man) cannot enter the Kingdom but that which is born of spirit can; the scripture at 1 Timothy could simply be taken to mean that no man (flesh) could approach God.
I would be genuinely interested to hear your explanation of how the scriptures that refer to heavenly rewards and existence are to be understood. Including the 144K scripture in Revelation where the location seems so clearly to be heaven. Also, both Jesus and Paul many times contrast the superiority of heavenly citizenship with earthly. See:
Matt 6:19,20 "Do not store up for yourselves treasures on earth, where moth and rust destroy, and where thieves break in and steal. But store up for yourselves treasures in heaven, where moth and rust do not destroy, and where thieves do not break in and steal.
Matthew 22:30 At the resurrection people will neither marry nor be given in marriage; they will be like the angels in heaven.
Luke 6:23 "Rejoice in that day and leap for joy, because great is your reward in heaven.
2 Corinthians 5:1 Now we know that if the earthly tent we live in is destroyed, we have a building from God, an eternal house in heaven, not built by human hands. 2Meanwhile we groan, longing to be clothed with our heavenly dwelling,
Philippians 3:14 I press on toward the goal to win the prize for which God has called me heavenward in Christ Jesus.
Philippians 3:20 But our citizenship is in heaven. And we eagerly await a Savior from there, the Lord Jesus Christ,
2 Timothy 4:18 The Lord will rescue me from every evil attack and will bring me safely to his heavenly kingdom. To him be glory for ever and ever. Amen.
Hebrews 3:1 Therefore, holy brothers, who share in the heavenly calling, fix your thoughts on Jesus, the apostle and high priest whom we confess.
Hebrews 12:22 But you have come to Mount Zion, to the heavenly Jerusalem, the city of the living God. You have come to thousands upon thousands of angels in joyful assembly,
Cheers
Artful