Remounting the display is a bit tricky!
Cleaning off fully all of the old tape adhesive and then making sure the solvent you used don’t leave a film so the new tape adhesive adheres to surfaces properly. Making sure there is enough pressure to pressing on the display to the frame and long enough. You also need to make sure the surfaces are warm enough for a strong adhesion (curing)
I’ve also encountered bent cases which I’ve had to straighten as any bend will cause the bonding to fail.
'''But that’s not going to help you now ;-{'''
When the display fell out things got damaged!
* The display its self: Glass cracked or chipped, the display connectors pulled out or damaged or attached cables cut or the connectors on them damaged.
* The main logic board: the connectors damaged and the connector could have pulled away from the logic board severing the connections.
From your description the backlight is not working but are you even able to see a faint image on the screen using a flashlight pressed on the glass at a sharp angle? Do you see any damage on the back of the screen when’re the cables are mounted and on the logic board (torn cable or damaged connectors)?
The fan running would be expected when there is damage in the sensor lines going to the display. The system goes into Safe Mode to make sure the system doesn’t overheat. It also slows the CPU clocking as well to reduce the heat it generates which is why your system is running slow.
How about taking some pictures of the back of the display where the cables connect and any visible damage along the cables. Also take a few pics where the cables connect to the logic board and the ends of the cables so we can see them too. [guide|21499]