In order to understand your examples some context would be useful, but let's see:
No conocí la canción.
This looks like it's missing something, like a subordinate expression, for example:
No conocí la canción hasta que tuve 40 años.
= "I didn't (get to) know the song until I turned 40 years old."
In this case it's plain that you do know the song now.
No conocí la canción cuando salió.
= "I didn't (get to) know the song when it was released."
In this other case it's a matter of context. With no further information, your hearer would probably ask: "Well, do you know it now?".
Alternatively, conocer can sometimes stand for reconocer "to recognize". If so, it would be as the speaker you consulted said:
No reconocí la canción.
= "(I heard the song but) I didn't recognize the song."
As for the verb in pretérito imperfecto:
No conocía la canción.
Since the imperfect refers to an unfinished process or a non-final state, this strongly implies that you do know the song now. But it's only an implication. If you are narrating a story in the past that mentions the song, this is what you'd say. For example:
Ella quería que cantáramos juntos, pero yo no conocía la canción. Ella se aburrió y se fue. Nunca la volví a ver.
Here you have just stated that you didn't know the song at the time that the story took place. Unless you give the hearer a clue, or flat out tell them that you looked up the song after the incident, it's unknown.