i had to replace the jack on one of my laptops it was such a pain to disassemble had to take everything apart including the monitor to get to it after i put the new one in and got everything working again i dropped the laptop and broke the screen -_- (oh kind of like your video)
the jack itself wasn't soldered though and simply had a 3pin connector and a grounding wire
so if you're going to do it yourself be prepared for a pita session and risking breaking the laptop or little parts of it like plastic tabs (i broke an end off the chassis of mine somehow etc)
i would just sell it to someone who wouldnt mind a little diy (include the replacement part)
and get a new one
repair shops charge something like $100 iirc so it just isn't worth it imo (at least for me when i was fixing mine)