Key cylinder or key?

I have replaced key cylinder & still have same problem. Turning key to off does not turn off radio, wipers,washer, clock lights, etc. If key is wiggled just a bit all will turn off but can't hold that position. I have 2 keys, one must be original and the other is a duplicate. Could it be the keys? The original looks well worn and duplicate binds in lock. I just bought the car for teenager and will most likely need your help again.