It sounds like the sides of the cabinet are absorbing moisture from the floor itself. Try placing the stopper in the sink strainer and filling the sink about one third with water, than turn the water off and pull the stopper up while observing the under side of the sink, especially around the strainer and the trap connections. If you find no leaks, run the dishwasher until it fills up with water, than advance the knob to the point when you here the dishwasher discharging water and observe the area where the discharge hose is connected to the strainer tail piece or garbage disposer inlet. Also, you may be getting water from around the area where the sink contacts the counter top. Check for small gaps or feel the sides of the bottom of the sink for any moisture.