The Old Testament is just as true as the New Testament. It seems that you don't understand what Jesus came here to do. You see, we learn from the very beginning of the Bible that God is JUST.
Think of it like this...
God is JUST, as a courtroom judge is just. He does not take sin lightly, just as if someone commits murder, a judge would not take murder lightly. And for that one crime alone (in this case, you, me -- the ungodly) deserve to be punished as a judge would have a criminal punished.
Romans 3:23, For all have sinned, and come short of the glory of God;
Like being sentenced for life in prison for murder, we deserve to spend an eternity in hell for what we've done. However, I do have good news, my friend. God is willing to forgive us; however, Jesus is the only way out, He is our escape key.
"And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory." -- 1 Timothy 3:16
God manifested in the flesh as the man Jesus Christ, and when he died on that cross, he took on the FULL PUNISHMENT for all of our sins, he bore the full extent of the wrath of God, he took our punishment that we so rightfully deserve upon himself. His blood was shed so that we may be saved.
"Hereby perceive we the love of God, because he laid down his life for us: and we ought to lay down our lives for the brethren." -- 1 John 3:16
God is offering a way out of hell, and Jesus is that way out!
You say you find it hard to believe that God would send people to hell for not believing in Him, even though they're good people?
Matthew 19:17, "...there is none good but one, that is, God..."
We've all sinned, and all fall short of the glory of God for that very reason. When Jesus died for us, that was enough satisfication.
Isaiah 53:10, "Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin..."
God is more than willing to forgive all, that is why Jesus died on the cross! God does not wish anyone to perish!
"Say unto them, As I live, saith the Lord GOD, I have no pleasure in the death of the wicked; but that the wicked turn from his way and live: turn ye, turn ye from your evil ways; for why will ye die, O house of Israel?" -- Ezekiel 33:11
"The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance." -- 2 Peter 3:9