The click noise is usually caused by dirty connections to your battery cables and/or your starter. A bad alternator will not cause the click but a discharged battery or a starter going bad will. My suggestion is to first clean up the battery terminals and make sure the battery to body ground is good. I would also attempt to see how dirty or corroded the starter is. Its barely visible under the intake on the rear of the engine. Maybe take some brake cleaner and spray it off. If none of that helps and the problem is still around take your car to an autozone or advanced auto parts and get an electrical check out done for free. If your battery is still good then the starter is the culprit.