One of two things, either the alternator is not spinning at all or the red wire at the back of the alternator is grounded. When you turn the key on and all of the lights light up it is because they are finding ground through that red wire to the back of the alternator. As soon as the alternator starts spinning it sends voltage up that wire and the ground goes away and the lights go out. What this means is that your idiot lights are finding ground down that red wire while the engine is running. If I was a gambling man I would put money on the harness melting down and the red wire being grounded out somewhere. Make sure your belts are tight, test your alternator and make sure it is putting out 13.5 volts or so and see if it can put out around 80 amps, inpspect your harness at the back of the alternator, diagnose and repair properly.

Mark