Look, it's really simple. "I" is the nominative case, although English grammarians prefer the term subjective case, of the first person singular, whereas "me" is the objective case of same, right? So when you are the object of the verb, you use "me", and when you are the subject, you use "I", OK? So "I went", you are the subject; "went with me" you are the object. The rules don't change when you add other people into the sentence. See? It's dead easy :rolleyes:
:D