1999 Ford Taurus

Electrical problem
1999 Ford Taurus Front Wheel Drive Automatic 138000 miles

Heres my problem. I'll be driving along for a while and then if I hit the brakes, use my turn signal, or do anything that requires power, my radio shuts off. Now given I listen to my music loud, however I do not have a huge system in my car. I have a Kenwood MP242 deck and stock speakers. Nothing extra. I do have the bass turned up a bit and when the bass hits, my dome lights, dash, radio, and headlights flicker. After tge radio shuts off once, it will try and restart but at the first sound of music it shuts off again.
This is what ive done already. I had the alternator checked by autozone. It was fine. I checked the battery when it was turned off and it read 11.4 or 11.5 volts. I think thats normal. Checked the ground off of my battery and it was fine but thats the only ground I have checked. I thought it was the radio so I got it replaced under warranty and rewired it and it still does the same thing. While the car was turned off I unhooked the positive battey cable for ten minutes and then started it to reset the car. None of that has worked. The only that has helped is when the car was running I unhooked the battery ground to see if it still ran. It did so I turnd it off, cleaned the terminal and replaced it and then started the car. The RPMs shot up better than normal with no stalling, no dim lights, and my parking brake sensor which hadnt worked started to wrork again. I took it for a test drive and it was great until a heavy bass song hit then it was back to normal. The electroncs I hav in my car are the radio deck and 2 cold cathode lights that I operate by a switch. Theyre 12 inches but dont take up much power. I have a cigarette light adapter that turns one into three so I can charge my ipod, phones and the cathode lights. Thats all there is to it and im just flat stumped. Please help me out.