This is actually a bad question as it is somewhat vague. As a result it is causing a bit of confusion.
The way the term belief as it is often used in the Bible and the way most people understand it today is usually very different.
In the Bible belief pretty much amounts to trust. As such it is not merely an academic exercise. If I call you and tell you to come and get $1000 from me: if you believe or trust me you will come and if you don't you will not.
Thus according to the Bible a person who believes is someone who keeps the commandments of God and a non-believer is a person who does not keep God's commandments.
Jesus explained that a person will keep the commandments of God if they love him. So love of God (which includes trusting him) leads a person to keep God's commandments.
So why do some people not love God? Well there are two main reasons. For one it could be that they don't know about him. The other is that they don't believe He can help them.
The first reason is easy to resolve so we can safely assume no one will ever go to hell for not knowing that God exists. The other is much harder to solve as it requires willingness from the non-believer himself.
For example some people believe everyone should be able to live their lives the way they want to without judgement. Thus the idea of a God who has commandments repulses them and they refuse to entertain the idea.
Others believe they know better than God so that even if they believe God exists they think he really knows everything about everything. They believe that sometimes their solutions are better than God's solutions or that God will not know the answer to a particular question they have. Many Christians fall into this trap. Unfortunately the only way out of their Non-belief is for them to take a leap of faith and do what God commands they do in a particular situation so they can learn for themselves that God really does know all things.
I could mention other things but all in all my point is that the type of unbelief that gets people into hell is not the accidental type. It is willful type of unbelief.
If nobody goes to hell by not knowing that God exists, why is He trying, allegedly, to reveal Himself?
The whole revelation thing (e.g. sending prophets, messiahs, missionaries and all) looks like a hide and seek exercise which is ultimately detrimental towards increasing someone's odds to escape hell.
it all boils down to the following questions: if I live a very moral life, without knowing about God or Jesus, will I go to Hell? If not, what happens if before I die I hear the stories of a Christian missionary and do not believe them?
Ciao
- viole