Now there are three things you will need to keep in mind... context, context, context !
Here's what I can say for a start :
in "que n'ai-je" there is the verb "avoir" in present tense with the first person (je)
It could also be followed by a past participle, which would make the sentence past tense.
the "que" at the beginning + the inversion and negation, express a regret, something the person hasn't done, something like "oh, why didn't I..." or "I should have..."