82 Buick Riviera Starting Problems

I have an 82 Riviera that is having trouble starting. When I try to turn the key switch to "start" it "clicks" off and all power is cut out. Then, there is absolutely no power to the vehicle--no lights, no window wipers, nothing. I have disassembled the steering column and the ignition rocker and actuator rods are OK. The ignition switch ohms out ok, so it's good. So the problem then rests under the hood. The thing is, it seems that when I leave the car along for a while and try again, I can turn the ignition on and get power, but as soon as I try to start it it trips off. There is an audiable noise under the hood like a relay tripping or something. Any help would be appreciated!