1995 Other Infiniti Models Starter/Alternator

The engine does not start for my 1995 Infiniti J30. The check engine light came on Sunday night and Monday morning the car didn't start. All I hear is one click sound and that is all. I checked the battery by taking it to autozones and the reader said it was good reading at 12 something. I've been driving on the original alternator and starter. Do I need a more powerful battery? I assume that my starter or alternator is the issue. Someone told me that it might be the starter solenoid. I need some guidance!