Can Non-Muslims qualify for Janna or Islamic Heaven?

Answer 1

NO. (Assuming that we are talking about Non-Muslims who do not convert to Islam.)

Answer
The Qur'an makes clear that ever since Muhammad's revelation of the Qur'an that all Non-Muslims are bound for the hellfire, see Qur'an 3:85, cited below. Additionally, in Sahih Muslim 153, the belief is affirmed that any person who hears about Muhammad and rejects him is bound for hellfire, also cited below. Many Muslims who wish to be ecumenical will improperly cite Qur'an 2:62, which argues that Jews and Christians who lived BEFORE Muhammad will go to heaven, cited below. However, Jews and Christians born after this point are hell-bound. (The clarity comes from the Arabic here which is in the past tense أمنوا as opposed to the present tense يؤمنون.)

Textual Sources
Qur'an 2:62: (Translation Sahih International): Indeed, those who believed and those who were Jews or Christians or Sabeans [before Prophet Muhammad] - those [among them] who believed in Allah and the Last Day and did righteousness - will have their reward with their Lord, and no fear will there be concerning them, nor will they grieve.

Qur'an 3:85: (Translation Sahih International): And whoever desires other than Islam as religion - never will it be accepted from him, and he, in the Hereafter, will be among the losers.

Sahih Muslim 153: By Him in Whose hand is the life of Muhammad, he who amongst the community of Jews or Christians hears about me, but does not affirm his belief in that with which I have been sent and dies in this state (of disbelief), he shall be but one of the denizens of Hell-Fire.

Answer 2

Yes. They can by believing in the ONENESS of Almighty Allah and converting to Islam.