"The computer has to be "On" in order to open the drive.."
Nope...Somewhere on the face of the CD drive you should see a tiny hole.
Stick a small wire (something like a paperclip that has been bent straight) and that will release the door.

I do a little bit of computer repair on the side as a hobby.
This past weekend I had three PC's I got back into shape.
Two would only boot to a black screen then power off (sounds very much like you), and the third had lost a lot of Windows funtions.
All three had the same problem....a virus...the same virus in all three.

The virus goes by the name "P2P_Worm.Win32.Polip.a" and attacks many of Window's files like Winlogin,Taskmag,bootin,Regedit, etc.
So far the only Anti-Virus software (AFAICT) that has a rule-set for it, is the one I use "Kaspersky Anti-Virus Personal Pro".

I had to do a fresh install of Windows to fix their problem(s)...the same thing your recover disk will do.
May not be your problem, but something to look into.

Chuck