Sometimes when starting my car several dash lights go on and off as the engine revs up and down several times. If the car is put in drive before the car starts revving up and down then the car will automatically accelerate a little. The battery has been replaced but did not help. Tests for the alternator (done by the dealer) show it running fine, at least after the car starts. See this video of the car starting for specifics
When you replace a battery in a nissan that has an electronic throttle body, you must perform a throttle body relearn procedure. Did you do that? If not, you'll wind up with a surging idle since it no longer remembers the home position.