Just had the same problem on my '78 280Z. I replaced the start switch. This is not the part with the key. This is a bolt-on to the back of the key unit. Cost me $27 at the Nissan parts counter.
Hope this helps
I had the same problem when I first got my Z. The locksmith said that most generic key places use the wrong key on older nissans. He made me a new one that looked totally different and it worked perfectly.
Replace the lock cylinder. I had the same problem. You need to take your old one off before you do this. The reason being is that some of the lock cylinders have a different turning radius. I think that there are 3 different ones. You will only know the correct one if you look at the back of it.
It is kind of a pain to get the old lock cylinder out. You need to follow the directions that come with the new one. You can pick one of these up for $20 bucks or so @your local Auto Parts Store.
If you have questions, let me know.
And Good Luck