I am not sure about your drive as I dont know it, but the disappearing green light could have 2 reasons I can think of:
1) the external psu has a defect and plugging it in causes a current which may make some (faulty) protection circuit kick in and turn of the psu
2) there is sth short circuited inside the drive and the psu shuts off correctly.
If you have the drive from a local dealer, he may be willing to test your psu with another drive or another psu with your drive. Depends on the dealer. Otherwise it would have to be sent in anyway.
Maybe you might want to try to unplug the psu from the wall socket, wait until its cool, plug it in the drive and then into the socket - of course only if the manual does allow it that way! I dont think you can destroy sth that way, but who knows. I know at least of a JVC surround decoder which burns a fuse if you dont use the soft poweroff (the one you can override with the remote control), wait a couple of minutes and then use the real power switch. Thats bad electrical engineering of course.
Sorry to hear of your problem and hope it ll be ok soon.