Kei te indicates that something is happening at the moment, and kāore... i te... indicates that something is not happening at the moment:
Kei te oma au.
I am running.Kāore au i te oma.
I am not running.
When it comes to an action in the past, for an active sentence (such as "I was running") the tense marker is i te:
I te oma au.
I was running.
We negate this sentence in exactly the same was as a sentence in the present tense:
Kāore au i te oma.
I was not running.
This means that a negation of the present tense and the past tense are identical:
Kāore ia i te waiata.
She is not singing.
She was not singing.
When one encounters a sentence like this, you will need to decide whether it refers to a past or a present situation based on the context, however, sometimes it will be unclear.
Kei te whakarongo au ki te wahine, engari, kāore ia i te waiata.
I am listening to the woman, but she is not singing.I te whakarongo au ki te wahine, engari, kāore ia i te waiata.
I was listening to the woman, but she was not singing.