I destroyed some of the wiring, but measured connections on the other stick, and used a thin wire to re-wire the broken connection from top to bottom. Works great, even could calibrate it without issues. Unfortunately I broke the thick wires soldering that connects the battery, I’ll need some more delicate equipment to fix that one, until then it works fine when connected to power with cable.
I know it’s been years, but I still have the machine alive and kicking, and I actually have an SSD there since a while. So yeah, that is indeed possible.
Thanks for the guide guys, managed to replace a broken HDD in no time. However, I'd like to mention that standard torx bits could not be used to remove the display, a normal screwdriver with replacable bits is too thick to fit in, and bits are too short, so you will need something thinner (or longer bits).