I had a 83 280zx that had this same issue. At times the car would not start and other times it would start no problem. when it wouldn't crank I would push start it. So evidently push starting it bypassed some of the system to crank the car. I'll skip the horror story I went through before solving the problem. The problem was the pick up coil in the distributor a $9 part in the 90s. What I found was one of the two wires going into the coil was broken only making connection at times. You couldn't tell it by looking at it, only when I took a small screw driver pressing against the wires the screw driver passed through one of the wires, after replacing it I had no more issues cranking the car. I would replace this part no matter condition it looks like. Good Luck!