Metallic Screaching Noise When Pushing Clutch And Brake

I just recently a '95 Mustang coupe from a used car lot last week. It has been running great so far, but now I am concerned because sometimes, when pushing the clutch at the same time as the brake, it makes a LOUD metallic screaching/scraping sound. I think it has happened a few times when just pushing the clutch as well. When this happens, my lights will also dim and the radio cuts out (the gauge for the battery will also drop, but immediately comes back up as soon as the sound stops). I am not a car expert by any stretch of the imagination, but if someone could give me some ideas as to what could possibly be causing this I would be extremely grateful.

Update- I just got in the car and had my foot on the brake as I pushed the clutch in and the car tried to start before I turned the key.. on the up-side I now recognize that noise and feel like an idiot..

Why is the starter engaging when I hit the brake and the clutch at the same time?

After driving some more I can confirm that it only happens with the clutch AND the brake, and only intermittently, as I drove quite a bit yesterday and some today without incident. I am going to get in there and check out the grounds and solenoid though.