Arduino-based water detection system, linked to something that controls the power to the dehumidifier. I could do this with my existing Vera automation system by adding about $15 worth of parts. 
Total cost would be around $190, but the controller could do much more than just run the dehumidifier ($130 vera, $30 Aeon power switch, ~$30 various arduino parts).
I'm sure there is a cheaper way to do it with just the arduino system(s), but I prefer to over-engineer everything...