1999 Ford Taurus replaced battery, car wont start

I drove my car earlier in the day and it worked just fine. When I went to drive it later in the day I put the key in the ignition and all of the normal electrical worked fine (ie dome light, power locks, etc) but when I turned the key to start the engine nothing happened but a click, in what sounded like the engine area, and all of the electrical component just died (ie dome light, power locks, even the button for the trunk) When I removed the key I could hear a faint clicking down by where the fuses are under my steering wheel. I immediately though it was the battery so I replaced it but it still happens. I cant even to begin to think what the problem is. If I walk away from it for a while and come back the normal electrical still works but again when I try to start it, nothing.