Would you mind presenting the list of verses you included in your study? I ask because I am wondering if you used only verses that have "hell" in them, or if you included verses that speak of eternal judgment without mentioning either Hades or Gehenna.
As to whether the concept of what is translated as "Hell" is a valid Biblical Doctrine, that is just an undeniable truth. Hades is not what most people think of when they think of "Hell," it is the Old Testament equivalent to Sheol, the place of the dead. It will not be until the beginning of the Millennial Kingdom that we see anyone cast into what is properly "hell," the Lake of Fire, which is the place of eternal judgment:
Revelation 20:11-15
King James Version
11 And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them.
12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.
14 And death and hell were cast into the lake of fire. This is the second death.
15 And whosoever was not found written in the book of life was cast into the lake of fire.
This is the "hell" that is often caricaturized by hollywood and confused with Hades by some (v.13 and 14).
Here is another description of the place of eternal judgment by the Lord:
Mark 9:43-48
King James Version
43 And if thy hand offend thee, cut it off: it is better for thee to enter into life maimed, than having two hands to go into hell, into the fire that never shall be quenched:
44 Where their worm dieth not, and the fire is not quenched.
45 And if thy foot offend thee, cut it off: it is better for thee to enter halt into life, than having two feet to be cast into hell, into the fire that never shall be quenched:
46 Where their worm dieth not, and the fire is not quenched.
47 And if thine eye offend thee, pluck it out: it is better for thee to enter into the kingdom of God with one eye, than having two eyes to be cast into hell fire:
48 Where their worm dieth not, and the fire is not quenched.
His teaching makes it pretty clear: being cast into Hell (Gehenna) has an everlasting duration. This type of terminology is seen in numerous teachings of Christ. We see a picture of enduring flames and corruption of the body (undying worms).
Here is another one:
Matthew 3:11-12
King James Version
11 I indeed baptize you with water unto repentance. but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire:
12 Whose fan is in his hand, and he will throughly purge his floor, and gather his wheat into the garner; but he will burn up the chaff with unquenchable fire.
I use the colors to show the correlation between the Baptism with the Holy Ghost which represents eternal life and the baptism with fire which represents eternal judgment. Again, the fire is never quenched.
Another example:
Jude 11-13
King James Version
11 Woe unto them! for they have gone in the way of Cain, and ran greedily after the error of Balaam for reward, and perished in the gainsaying of Core.
12 These are spots in your feasts of charity, when they feast with you, feeding themselves without fear: clouds they are without water, carried about of winds; trees whose fruit withereth, without fruit, twice dead, plucked up by the roots;
13 Raging waves of the sea, foaming out their own shame; wandering stars, to whom is reserved the blackness of darkness for ever.
For ever is pretty clear.
One more:
Matthew 13:39-41
King James Version
DID
39 The enemy that sowed them is the devil; the harvest is the end of the world; and the reapers are the angels.
40 As therefore the tares are gathered and burned in the fire; so shall it be in the end of this world.
41 The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity;
This one has, in my view, an application to both the end of the Tribulation (and the start of the Millennial Kingdom) as well as the end of this current Universe (and the beginning of the Eternal State where we will dwell in the new heavens and Earth). But it still speaks of eternal judgment.
The demons asked Jesus if He had come to torment them before "the time:"
Matthew 8:29
And, behold, they cried out, saying, What have we to do with thee, Jesus, thou Son of God? art thou come hither to torment us before the time?
This doesn't present the picture of them being snuffed out, but one of ongoing torture. (Gehenna) Hell was created for Satan and his demons:
Matthew 25:41
Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
And when Satan is cast in we see he—
Revelation 20:10
King James Version
10 And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.
For ever and ever torment doesn't exactly agree with the notion of annihilation.
God bless.