Hey knc1, just an update to let you know how it worked out.
I finally got my hands on a hot air soldering system with a small opening (about Ø4mm) but as much as I tried to be careful I still melted the surroundings a little bit (the transparent LED stripe and the black part of the housing). Maybe it would work when the screen and the LED stripe are separated from the housing but I didn't want to take the risk in doing so.
But what worked was placing a tiny amount of tin next to the loose pin of the sensor (in my case the bottom right pin) and holding the tiniest SMD soldering iron I could find next to it. It didn't work right away, since there's a white plastic sheet that covers the pins. But after 3-4 attempts the tin made it's way around the sheet and now my Kindle finally behaves normal.
Thank you once again for helping me with one of my devices. If it weren't for you, i probably would have just desoldered the sensor and ruined my PW
