Welcome to the forum.
First thing that I would look at would be the manual eject for the multi-drive, which is usually a tiny hole in the unit, that is activated by a straightened paper-clip, or similar.
Have you tried to use the software eject? If that doesn't work, try turning off your anti-virus software. I have just had the same problem - wouldn't eject mechanically or via software - as soon as I turned off the McAfee virus scanning the problem went away.
Thanks for that major contribution related to your McAfee virus scanning and its impact on some DVD functions.
I see you helped here and in another thread related to this matter.
This seems to be an issue which should be popping up with greater frequency.
Thanks for sharing.