Car radio wont start and requires car restart

My car radio/stereo acts funny. Recently installed JVC KD-HDR40, along with Scosche GM2000 wire harness on my 01 Pontiac Grand Am. Sometimes when I start my car, the stereo wont turn on, no matter how much I press, or press and hold, the power button. However, If I press the display button, it will light up, and display the time for about 5 seconds, and then turn back off. The only way to start the stereo is by turning my car off and restarting it. The stereo will then turn on. And here's another situation. Sometimes, when the stereo is off, in its faulty mode when I turn the car on, as soon as I turn the car off(to restart), it will start up and play music. If I then turn the car back on, it will shut off. In such a scenario, I open the driver side door to turn the stereo off (Because I think the stereo has now powered on, and if I start the car, it will turn back off). I have to keep playing around till it thinks in which mode the car is in operation. Seems like it is confused between what is off and on. I called JVC and they told me to reset the unit. I did that, lost all presets, but no change in its weird operation. Somebody please help! Is it the wire harness? The wire harness model was given to me by a rep from Sosche. Also, I do not have Bose or Onstar installed. What do you think is happening and why? How can I fix this?