I think my VESC died due to vibrations over time. One of the pieces of the VESC has broken from the board. I was wondering if it's possible to connect this back up? If so how do I go about it? I'm not that great with soldering but this is a pretty large item. The main thing though is knowing the orientation. See pictures below for the details.
Interesting, it is the first time I see this happen. The inductor is for the 5V regulator that also drives the 3.3v net, and I think it will work fine once you attach it again. It could be that the inductor itself broke, so it might not be possible to solder it. You can give it a try at least. The polarity does not matter, you can solder it in any direction. In case it is broken you can get a new one, the part number is XAL5050-223MEC and can be bought from e.g. mouser.
Before you put the VESC together you should replace the thermal pad with a new one to avoid shorts as the FET cases are connected to the motor phases and battery +. Something like this should work:
https://www.ebay.com/itm/Phobya-0-5MM-W%C3%A4rmeleitpad-XT-120x20mm-7W-m...