[rewboss]

It depends who you ask.

A traditionalist would say that since the phrase is an answer to the question "Who will help me...?" (if this is the story I think it is), the personal pronoun in the answer must be a subject and must therefore be in the subjective form: "Not I."

A more modern view is that when there is no verb actually present, English uses the objective pronoun (analogous to the way that, for example, French would use moi instead of je in the same situation): "Not me."

So a traditionalist would say that "Not me" is incorrect, while modern thinkers would tell you that "Not I" sounds affected and pretentious.

As it is, "Not I" is now almost never heard in speech and rarely seen written. It is now considered to be old-fashioned.