Hello,
i dont have much time to help you with your problem, but i can tell you what first comes on my mind when i read your text. Your wire, if other end is in the air, can collect some noise from everywhere when its floating like that. so, if you want 0 on your input, connect it to the ground and check your output. If output falls to zero when you connect input to GND, the problem is solved.
If this help you, award me, if not, ignore.
good luck with your project