I t appears that the drawer mechanism has failed. You have tried all the options I would have suggested. The only thing I can think of is that there are normally 2 x small springs attached to the flap - one of these may have become dislodged. A straightened paper clip is what you need for the small hole (not a pin) if you want to try that again. Failing that open up your case (unplug the power supply first) and remove the drive by removing the attached leads and slide out. You may be able to fix better with it removed. Other than that it may be time to replace the drive - not expensive these days.
Fujitsu Lifebook P727 laptop review