I will start by letting you know that I dont really know what all of the components on a driver do. My skyray S1 stopped working the other day. When I pulled it apart I saw that the little coil had fallen off. I took the positive wire off the driver and reconnected to the first solder point that held the missing coil. The light works great on a 10440 now but wont work on a AAA. What exactly did I do? Is the coil responsible for boosting the voltage?
LED driver expert I am not, but do have an electrical background. A coil is definitely a key part in a "boost" circuit. As you know, you must overcome the forward voltage of the LED for it to light. This matches what you are seeing, no light at 1.5V (AAA) and light at 3.6V (10440).