I'm having a similar problem but I'm not sure what to do about it. Someone who owned the car before me put in an aftermarket stereo, but took it out and put the stock one back in (as shown below). I got some stock plugs from a junkyard and wired up the stereo using colors and a diagram.
I pulled the cover off the back speakers and they're pioneer speakers so I'm assuming the ones in the dash board are too, and none of them are blown.
I was driving around today and like the speakers would start to pop and crackle, and if I turned the stereo off, it would stop. So definitely something to do with wiring/stock unit (which is a head unit right?

) Not only that, I have to turn the volume up almost as loud as it will go to even start to hear it, with the windows and t-tops up. The facelight of the stereo won't light up either when you turn the lights on.
Please let me know what might be going on.