How to connect a switch to a microcontroller in an extremly noisy environment
This was bumped to top but I presume the problem has been long solved, one way or the other, still in general here are some thoughts of dealing with very noisy signals. 

The very first thing that comes to mind is: Why are the signal and power wires running in the same cable? Is there any reason why you couldn't do that with a separate shielded cable? That cuts the near field coupling right out. 

If that doesn't work or is not allowed for some reason, you can add common mode chokes to the control lines. That's explicitly designed to take out noise that's coupled to both wires as in your case. 

Beyond that, you need some kind of capacitor with a button to suppress the button bounce and you could make that a simple RC low pass filter while you're at it. That can be arbitrarily low frequency althought going to megaohms is probably not a good idea. (100nF * 1meg =  100ms time constant or 1.6Hz corner frequency. Likely that'd stop the button working properly since you'd have to keep it pressed for a good while but 100nF + 100k would have 5x time constant of 50ms that should be good enough.