Electrical Issue on my 92 Ford Crown Vic?

[Cameron]

Alright, I have an electrical problem on my 1992 Ford Crown Vic (4.6 SOHC V8). I had the battery checked and it is fine (per AutoZone on battery tester; 12.8 V at rest). The battery cables are all in decent shape and have good connections. If and when the car starts and runs, the alternator charges at a solid 13.8 to 14.5 volts, so that seems OK as well. The problem comes when I go to start the car...acts like a dead battery. Starter won't turn over, not even a solenoid click. Dash lights are dim. If I jump the car, it will start and stay running even after I disconnect the jumper cables. As soon as I put any decent load on the system (i.e. turn headlights on, hit the brake lights, etc) the car will die and go back to the "low battery" syndrome (even though it reads a solid 12.8 V at rest). I put a volt meter on the battery and it reads 12.8V at rest. Even the ACC key position will still run small loads like the radio. But as soon as I put the key in the ON position, the volt meter drops to like 4 volts, almost as if I had started the car or put a huge load on the battery. I was thinking maybe the ignition switch, but not sure. Possibly a major loose connection, but where do I start on this car? Bad Fusible link connection somewhere? I'd imagine whatever part is causing the problem is getting very hot due to the apparent load on the battery/power system. ANY IDEAS WOULD BE APPRECIATED!!!!