Dative?

[miconazole.livejournal.com]

Hi everyone!

A while back someone posted "Чем мне кормить мою семью" and "Мне не прокормить семью на эту зарплату" as translations for "How can I feed my family" and "I can't feed my family with these wages." Now I must have missed some major concept in Russian grammar because I often see constructions like these and I don't get why it's мне and not я. Can you enlighten me? :)

PS Is it possible to use the nominative in these sentences and still get the same meaning? e.g. "Я не смогу прокормить семью..." or is that horribly awkward or something?

Edit: Thanks! :DD