It's my daughters car ,she drove it to work and after work it would not start. Could not figure it out

so we towed it home. The first thing I checked was the fuel pump because when you turn the key to the on position I did not hear the electric motor start up. Figured that was it,wrong. I removed the fuel lines at the pump and decided to try the key to the on position and nothing happened, but soon as I tried to start the engine gas was flowing out of the pump. So of all my cars, this is the only car that does not turn the fuel pump on when you turn the key to the on position prior to cranking the motor.Anyways took the fuel line off at the fuel injector rails to make sure the flow made it there,yes it did. Okay,now check for spark.Took coil wire from distributor cap,no spark. Checked coil with Chilton procedures and it checks out. So why didn't I get a spark out the end of the wire when turning it over. Now it basically says if coil checks out go to pick-up coil.Sorry for the long-short of the story,but this is where I'm at now

.Sorry it's a 4 cylinder 1.6 litre automatic.