|It's strange the eject button doesn't work, as the drive powers up with the BIOS.|
Nor can I see why having the disc inserted in the drive makes any difference to the system,unless, maybe, it's a corrupt disc which is somehow crashing the system.
I wont comment on the other issues, but to remove a disc from the DVD drawer, simply straighten a paperclip, insert into the pinhole in the drive's facia and gently push. You'll feel some 'spring resistance' before it moves in a tad.
This will unlatch the drawer.