I read the definition of Dukkha on the site you linked to, to make sure I knew where you were coming from.
Here's my humble attempt at an answer, based on the Scriptures I believe in.
Death is the direct result of sin.
Romans 5:12
Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned:
Suffering in this world is because of the fallen state of this world. And of course many times a person will suffer or endure something like a disease or something, and it has nothing to do with any particular sin that they committed. So suffering in general isn't necessarily due to a particular sin the individual committed (although sometimes it is exactly that), it is also due to the general condition of this world being in a fallen corrupted state.
Romans 8:21-23
21 Because the creature itself also shall be delivered from the bondage of corruption into the glorious liberty of the children of God.
22 For we know that the whole creation groaneth and travaileth in pain together until now.
23 And not only they, but ourselves also, which have the firstfruits of the Spirit, even we ourselves groan within ourselves, waiting for the adoption, to wit, the redemption of our body.
So pain and suffering is the result of sin. Even the ground was cursed because of Adam's sin.
Genesis 3:17-19
17 And unto Adam he said, Because thou hast hearkened unto the voice of thy wife, and hast eaten of the tree, of which I commanded thee, saying, Thou shalt not eat of it: cursed is the ground for thy sake; in sorrow shalt thou eat of it all the days of thy life;
18 Thorns also and thistles shall it bring forth to thee; and thou shalt eat the herb of the field;
19 In the sweat of thy face shalt thou eat bread, till thou return unto the ground; for out of it wast thou taken: for dust thou art, and unto dust shalt thou return.
So the resolution of suffering is the resolution of sin. To get rid of suffering, sin needs to be gotten rid of.
This is exactly what Christ did on the cross. The cross was the reason Jesus was sent here. When He died on the cross, He took on all the sins of everyone who would ever believe on Him. And to those who do believe on Him, He washes away our sins, and not only that, but He gives us His righteousness (which is completely sinless and absolutely perfect.)
Colossians 2:13-15
13 And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;
14 Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;
15 And having spoiled principalities and powers, he made a shew of them openly, triumphing over them in it.
And everyone who does believe on Him is given eternal life.
John 6:47
Verily, verily, I say unto you, He that believeth on me hath everlasting life.
And as for suffering and death, we deserve it, because we have all done wrong. But Jesus suffered and died, not for His sins, but for ours.
Luke 23:40-42
40 But the other answering rebuked him, saying, Dost not thou fear God, seeing thou art in the same condemnation?
41 And we indeed justly; for we receive the due reward of our deeds: but this man hath done nothing amiss.
And as for eternal life, how could there be a greater resolution to suffering and death?
Revelation 21
1 And I saw a new heaven and a new earth: for the first heaven and the first earth were passed away; and there was no more sea.
2 And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband.
3 And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God.
4
And God shall wipe away all tears from their eyes; and there shall be no more death, neither sorrow, nor crying, neither shall there be any more pain: for the former things are passed away.
5 And he that sat upon the throne said, Behold, I make all things new. And he said unto me, Write: for these words are true and faithful.
6 And he said unto me, It is done. I am Alpha and Omega, the beginning and the end. I will give unto him that is athirst of the fountain of the water of life freely.
7 He that overcometh shall inherit all things; and I will be his God, and he shall be my son.