The subject of the sentence, simple or compound, must be in nominative case. "I" is the nominative (or subjective) case pronoun in English. "me" is an an objective pronoun. It functions as a recipient of action or as an object of a preposition. "Billy and I" is a compound subject which must be in subjective/nominative case. "Billy and me" cannot be a compound subject; can only function as an objective pronoun... e.g., "he gave the book to Billy and me." (recipient of action) "This is a picture of Billy and me" (object of the preposition). Or as float puts it --- This is a picture of Billy. This is a picture of I. .... ? really? This is a picture of Billy and I. .....Yeah, that's why people who say this sound like ****ing retards. But, most folks come by it honestly. Kids no longer learn much grammar in schools these days. This is why you hear people (and some of you are on this board, but I presume are being sarcastic) saying things like "I should have went"... "We would have gave"... "They should have knew..." .... "Come to Billy and I's party..." There are national news anchors making millions of dollars a year who regularly use this kind of bullshit language.
Probably the hardest thing about learning italian has been trying to remember what all the damn tenses and whatnot meant in English much less italian