Thanks for asking, and may Allah reward you for asking. I have taken some (if not many) points from Dr. Zakir Naik lectures, and will try in due course to make those points as brief as I can. So lets get started.
- Every person is a born as Muslim. Any deviation from his natural "fitrah" is due to teachings of his parents, and/or external enviromnet
- Supposedly for argument sake a non-Muslim dies and he starts complaining on Day Of Judgement "Why didn't you give me a chance to guide me to Islam?". This is a valid question but there is a flaw that Allah is unjust. Allah is,not unjust in the least of degree. Therefore, we must establish that Allah just and wise.
- Hence from earlier point we can conclude that Allah does give every non-Muslim a chance in his life, as mercy and justice on his part, to revert back to a Muslim; he gives him light towards the true path. Look at mike, even though he is atheist, he knows about Islam (though there are points I don't agree with him, I respect him), as an example in practice.
- If Allah guides that man, that doesn't imply the person becomes lazy in achieving the objective i.e. coming back the true path (Islam). That would be like saying a teacher gives right sources (books) to study your exam but you don't actually strive in reading through books. So ultimately the student fails. Similarly Allah gives you the light to guidance, but you must strive (jihad). This is a fact, not an opinion: And as for those who strive in Our path-We will surely guide them in Our ways. And verily Allah is with those who do good.[29:70]. In addition we must make sure that the sources are right: Quran and the authentic Sunnah, if you find difficulty in understanding then referring those references in Quran and/or Sunnah to a learned scholar who is trustworthy. Therefore it is our duty to strive in knowledge of Islam (which helps clears doubts) and present Islam to non-Muslims in the best way possible. See this outstanding verse about knowledge: "Say believe in it (the Qur'an) or do not believe. Verily! Those who were given knowledge before it, when it is recited to them, fall down on their faces in humble prostration. And they say, 'Glory be to our Lord! Truly, the Promise of our Lord must be fulfilled.' And they fall down on their faces weeping and it adds to their humility." [Al-Qur'an 17:107-109]
- I will make this a valid point from an answerer: the man is not to blamed for his nature, but rather for following his nature! which is a major differentiation between a man and an animal.
- If you were the only person in the world then Allah will still guide you as part of his mercy. You should avoid doubts in Allah. He will show you signs to guide you: We will show them Our Signs in the universe, and in their ownselves, until it becomes manifest to them that this (the Quran) is the truth. Is it not sufficient in regard to your Lord that He is a Witness over all things?[41:53]
- Had there been a need of another Prophet, Allah would have sent so. But prophethood ended with Prophet Muhammad (saw) which implies that message is complete and the Islam is spreading with power and mercy of Allah (if you see the Quran has been preserved till now for this very purpose). If you know, it is a fact that Islam is spreading as the fastest religion in the world thus it must impact every non-Muslim in one way or another as part of guidance (a chance to come to the truth) by Allah. So injustice is impossible, in this world, by Allah, neither in the world to come.
To conclude my answer the only one blaming himself will the sinner himself. He will surely be shown signs by Allah (this is a fact) and will only ask for more respite, but it will be too late for that. The following verse is conclusive:
7 When they are cast therein, they will hear the (terrible) drawing in of its breath as it blazes forth.
8 It almost bursts up with fury. Every time a group is cast therein, its keeper will ask: "Did no warner come to you?"
9 They will say: "Yes indeed; a warner did come to us, but we belied him and said: 'Allah never sent down anything (of revelation), you are only in great error.'"
10 And they will say: "Had we but listened or used our intelligence, we would not have been among the dwellers of the blazing Fire!"
11 Then they will confess their sin. So, away with the dwellers of the blazing Fire.