odd audio issue in 1998 Toyota corolla

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Did you cut the factory wiring harness on the car?? If you did, I would go to a junkyard and cut a harness out of another car to put it back to factory condition. Then use a cable like this to connect it: http://www.metraonline.com/part/70-1761

Don't use butt splices, they're terrible if you don't have a good crimper. I would solder the wire for a better connection, this can be done on a bench from the comfort of your house if you use a harness like I linked above. Once all your soldering and heatshrink is done, then bring it out to the car and it should plug and play.