I have had the starter, alternator, and a new battery installed in my 1997 Nissan p/u 2.4 automatic and it just gives one click and won't start. the headlights don't dim and all accessories work. what could be wrong?

Your ignition switch should be fine, as if it were not functioning properly you would not even get a click. It only supplies very low-amperage 12v to the starter relay, which I suspect is your problem.
I believe Nissan's pickup model has the relay on the passenger side of the inner fender. It is most likely the defective relay that you're hearing the "1-click" from.
I'm also assuming the new starter has a new starter solenoid on it, and not simply the old solenoid re-installed on a new starter.

Most likely your ignition switch.