Lights flashing at idel and over 3000rpms

hey guys I been looking all over the forums for something but have had no luck. when i start my car all my lights are dimming and flashing. i have a pretty nice audio system in my car but it does it with all my amps turned off. i am thinking my alternator is causing all the problems. the 2 White (yellow) wires that screw onto the alternator are burnt up and wire is exposed. i taped them up but that didn't fix anything. there is also a skinny wire with a blue rectangle plug on the end of it that is just hanging down there, i cant figure out where it goes. i want to rewire the alternator up to the battery with a thicker gauge wire but i am dumb and really dont know what im doing. im an car audio installer but never really did much with alternators. any tips? Any idea why the lights are flashing? i know its not the battery cuz it was doing it before i changed it to a optama red top. by the way i have a 1996 Talon Tsi awd turbo.