My very first reaction to that symptom would be: make sure that the power cable is plugged into the drive. The fact that the little green light comes on suggests that it is, but I'd open it up and unplug/replug both the data and power connections to make sure they're secure just to be on the safe side.
Failing that, it's possible that the tray mechanism is jammed somehow - try what WyomingKnott suggested to see if that frees it up.
The only other thing I can think of is that some devices have a "shipping pin" to immobilize moving parts until the device is ready to be used. I've never seen an optical drive with one of these, but there's always a first time - check to see if there's any pin or tag or tape (could be transparent!)...