In other words, "ich" and "mich" are both first person singular pronouns, but just like in English, you choose one based on the case, or the role it plays in the sentence. "Ich" is the pronoun for nominative case, meaning that "ich" is the "subject of the sentence" as we'd say it in English grammar.
Ich = I Mich = me
Me like the newspaper. - incorrect English I like the newspaper.
The Newspaper likes me. The Newspaper likes I. - incorrect English
I is a subject pronoun, so by definition, it IS the subject when used, making the newspaper be the Direct Object.
German word order is a little loose (except for the Verb), so you must deduce which is the subject and objects by acknowledging the Pronoun cases, such as subject pronouns: ich, du, er/sie, wir, ihr, Sie/sie
That's so funny that you said, "Unless you live in Pennsylvania"!! I am currently living in Germany, but Ich komme aus Pennsylvania und "Your newspaper, I like" sounds like gut Englisch to me. It sounds more direct. But, of course, intuitions vary widely across people and landes.