Hot wire your starter solenoid, if that doesn't work take it back to wal-mart. If it does then it has to be between the ignition and the solenoid.
I have a 280zx that had the same problem, I fixed it by replacing a wire to the solenoid.
Just take the power lead to the starter and connect it directly to the battery. if it cranks than the strter is fine, and you have a wireing problem. I have the older z so the wires are all different, but with the sasme problem, i found a bad connection between the engine harness, and the main harness, under the dash