Your experience in the Marines was similar to mine in the Air Force twenty some years ago, when I was, if not an atheist, a non-theist at least. (In other words, I didn't have much need for, therefore, no thought of God.) The "forced march" to the base chapel during basic training was strongly encouraged, though in fact optional. The only difference between your experience and mine is that our training instructor left us alone in the barracks.
(Of course, Air Force basic training was not exactly, ahem, rigorous. We did not have to march when it was too hot and our physical fitness test consisted of running in place for fifteen minutes. Mind you, Byron, we normally would have had to run two miles out on the base track, but it was raining the day of our test.)
However, I must admit that it was my Air Force experience that sparked my interest in religion. I was an airborne cryptological linguist, which meant attending the Air Force's survival school at Fairchild AFB in Spokane, Washington. (After which I was spared an assignment to Okinawa and sent to England instead.) Part of my training at Fairchild included P.O.W. resistance techniques. There I encountered veterans who had been "guests" of the Hanoi Hilton. Again and again they told stories of how their religious faith gave them the fortitude to endure captivity.
While I was confident I had the right stuff without faith to endure such a trial, their stories of faith were not easy to dismiss. Indeed, the power of the faith of P.O.W.'s should not be dismissed as mindless evil superstitions; it requires an examination more serious than knocking down cartoonish strawman as some Objectivists are wont to do.
Bill a.k.a. Citizen Rat