Intermittent no power and clicking at passenger kick panel?

Hi, I own the car listed above and I am having some issues when I go to start the vehicle. I'll get clicking noises for a couple times and then one loud click, it seems and then it stops. Then no power at all; no radio, no lights, no brakes, no wipers, nothing. Afterwards I'll take off the battery terminals and let it sit for a little while and it seems to reset the vehicle somehow if I just give it some time. Then I'm able to try again and eventually it starts. I've already replaced my starter, alternator, battery, distributor cap and rotor. The vehicle's pretty simple I checked the voltage coming out of the starter solenoid and I'm okay there. I checked my fusible links; I checked all my fuses. Someone had mentioned something about a sensor past the firewall on the passenger side and there seems to be a missing male end which I'm going to replace if that doesn't work. Do you have any other ideas?