"Mhínigh mé an scéal ach níor éist sé."
Translation:I explained the story but he did not listen.
Not here. Ní is the present/future/conditional tense negative marker, níor is the past tense. However, there are 6 irregular verbs that do use ní in the past tense.
Is "he didn't hear" an acceptable translation? Rather than 'listen'? Anyone know?
Yes. The do that used to indicate the past tense only survives as d' before vowel sounds (some speakers of Munster Irish still use it for all verbs), and is not used when you have a negative or interrogative particle.
The r in níor and ar indicates the past tense.