1998 Volvo V70 Starts, Drives Then Dies In Action

Engine Mechanical problem
1998 Volvo V70 All Wheel Drive Automatic

My Car's Been Pretty Amazing but A Week Ago I Was Driving And Then A second Later Outta No Where Goin About 30MPH Its Dies. Power Still on, But The Engine Turns Off.
I Pull Over, And Turn The Key Off, Then Back on N Cranks Up, Trys but Seems Stuck. Soon I See That The Battery Is Dead, I Leave It on The Street It Died On, N Disconnect The battery, The Next Day It Starts Up Fine N Drives 3minutes Then Dies Once More, Doesnt Start After That. A Few Days Pass I Think Its An Alternator Problem So I Buy A New Battery It Starts Fine, I Unhook The Cables To The battery N It Still Running Off The Alternator, So I Drive It Down The Drive Way N It Shuts Off. And Doesnt Start Anymore, Its Trying, POwers Good, N Its Crankin, But Not Getting To That Start point. I Need Help. My Last Guess Is My Fuel Pump, N Is There A Way To Find OUt, With Buying N REplacing It Since IM On A Tight Budget N The New Battery Already set Me Over? Thanks For Any Help