So, the starter motor turns the engine, but the engine doesn't want to fire? Have I got it right?
Nissans are VERY sensitive to voltages. A battery may start the car, but then the alternator expends so much of its output re-charging the battery that the ECU thinks there is a problem and the car runs like crap.
The other thing is that the ECU needs a minimum voltage (somewhere around 7V) to be "alive". If the starter motor drains so much voltage that the voltage available to the ECU is less than this critical value, then the engine might spin for ever, but the ECU isn't alive to fire everything off.
If you ever have troubles with starting and batteries, the usual fix is a new battery.