About a year ago I dropped my pi 3 (in a case) and the sd slot peeled up half way as well as the sd card falling out, it is obviously broken I have tried to super glue the metal sheath back down to no avail as well as use a different sd card (the dropped one would heat up when plugged into pi, probably broken). I also tried soldering a short where I thought the sd detect switch connected (poor soldering skills might be part of issue) but still no function. If I could just get the pi to boot once with the new config.txt parameter for usb booting I would definitely boot over usb.
p.s. I do not have easy access to an hdmi display and the closest I can get is av input on one of those portable car dvd players.