Grinding when clutch is completely depressed

Here is the sequence of events:

1) Car starts fine, but I notice that the e-brake light on the dashboard is on but really dim.
2) The car drives fine until the first time I hit the brakes and push in the clutch all the way.
3) I hear a horrible grinding noise from under the hood. At the same time the radio faceplate goes blank.

The noise will continue until I turn off the engine, or release the clutch slightly. I can hear the grinding when shifting gears and the radio will cut out at the same time. This does not happen every time I drive it, but I know it will when I see the dim brake light on the dashboard. I figured out that not depressing the clutch all the way would avoid this problem.

My theory is that the starter motor is grinding on the flywheel continuously when the clutch is fully depressed. The electrical system seems like it "knows" that the starter is going and cuts power to other accessories.
For now I plan to drive the car without fully pushing in the clutch except to start.

Has anyone ever heard of a similar problem, and what component caused it?

if that thoery is corect, wouldn't the flywheel cause that? push on the clutch and it moves the flywheel into the starter bendix.

could be something else though.

Probably is. Just thought I'd throw that out there before bedtime for you to ponder.