I know this is old and you probably have it figured out now, but you raise a good question, so I'm posting here for anyone else that gets confused by this sentence. Multiple comments below are wrong.
Short answer: No, use the imperfect tense to say "I was going..." "Iba a cerrar la puerta."
Long answer: I think you're combining tenses to get your translation. "Ir a + infinitive" does mean "going to..." and "fui" can be "I was" or "I went," as it's either "ser" or "ir," but not both at the same time. Keep in mind it's a preterite conjugation, so it's a specific event beginning and ending in the past. "Ser" makes no sense in this sentence, so you shouldn't think "I was" because "ser" gives us the wrong kind of "I was." That means "fui" is conjugated from "ir" in this sentence, so it means "I went." If i want to say "I was going," I say "iba."