Definitely check battery connections and alternator output...
"It makes a clicking noise like the turning signal is on but isn't on. "
When it makes that sound, just SLIGHTLY touch the directional lever up or down.....if the noise stops, you need a new multifunction switch.....also, if the your directionals don't work, press the hazard flasher, on then off....if the directionals work now, need a hazard flasher......there was a recall for this....
As GMtech1 asked, check for after market accessories.......
I am not sure of the wiring circuit for this car, but it's also a possibility that you may have a BCM problem....