Have you got a voltmeter to measure the voltage across DO and ground with the switch open and closed?
Or alternatively, stick your led and series resistor across DO and ground, with nothing connected to the Arduino except maybe borrowing its 5V and ground to power the module.
In fact, I wonder if one of those components on the module IS an led, if so what does it do?
And as a very last resort, have you found any documentation for that module 
I wonder what its potentiometer does: perhaps it's some kind of sensitivity thing to adjust the line between digital high and low, maybe it needs moving.