1999 Ford Expedition Will Not Start

I just spent the morning driving about 150 miles, and when I came back out to start my vehicle it was dead. I cleaned and reconnected cables to my battery and that didn't help much. Radio and wiper blades still work. The crazy thing is that when the keys are not in the ignition I hear a very loud clicking sound near the fuse box. Since I know virtually nothing about cars I pulled out fuse 15 to see what would happen. Immediately the clicking sound stopped. I do not know if this means anything, but the clicking sound by my fuse box does not stop. I went to my vehicle after 30 minutes to see if there were any change and it was still making that clicking sound. Any suggesstions. Alternator replaced 3 years ago.