'simple present tense verb' or 'infinitive'

You should say "infinitive" because that is what it is. The simple present of verbs varies in the 3rd person singular, but not the simple past.

("He has" / he did not have" etc)

The negative simple past tense of every verb except "to be" is formed as follows:

did not + the infinitive of the verb.

The negative simple past of "to be" is formed from the affirmative simple past + "not"

Singular:
I was not
you were not
he/she was not

Plural:
we were not
you were not
they were not

Thanks, Contrex.