I was playing with my dongle and discovered that if the USB cable is not plugged all the way in, the red LED will come on, but the green LED wil not. When I pushed the connector in the rest of the way, the green LED came on within 1 second (it beat the windows recognition tone). This is with the driver installed, but no applications running.
Apparently the power pins make contact before the data pins (that makes sense from a reliability standpoint), but the DMX transmission does not start until after the device driver is initialized. Once started, the DMX transmission runs continuously, regardless of whether or not data is being sent to the dongle.
If that does not solve your issue, I would take a voltmeter and make sure that the capacitor has something close to 5v across its leads. The red LED looks like it is powered directly from the USB module, but the green LED requires everything else to be working...
Good luck!
RM