Will Sosa

I own a 1995 Acura Integra LS. I'm having some issues with my aftermarket car stereo. It doesn't turn on right away after the car has started. The radio is brand new. And when it does turn on and I turn on the headlights it turns off or sometimes the radio doesn't turn on at all. Then I jiggle the keys in the ignition while the car is on then the radio sometimes comes on. Can you please help me with this problem or make some suggestions please?