Inductive spikes upset Interrupts
I'd suggest building a Faraday cage around the inductive coil. It's probably inducing enough current in all the wires around it to trigger logic level voltages in your signal wires, in the board, etc. 

It sounds like the goal is for the coil to fling a magnet away, so you might have to settle for a "Faraday bowl" (an open-topped Faraday cage). Some magnetic field would leak out the top of the bowl, but if you place the control board below the bottom and several feet away it might be enough. 

You might need to shield everything separately: Faraday cage around the Arduino. "Faraday Bowl" around the coil. Coax cables for everything, where the power to the coil is in a coax cable that's grounded separately, etc.