OK, looking at this, I’m pretty sure you should buy a ribbon cable. The question is, what is the correct size. You’ll have to bring this to Sim Lim Tower. The cable should be very cheap (under $2), but finding the correct size will take time.
Also, is the tip of your soldering iron sharp enough? Do you have 0.4mm solder? Thick solder wire will leave big, clumsy pools and due to their size they are hard to heat properly leading to the sticking problem.
Like the posters above, I am most concerned about a short. You see, your first picture is very dangerous. There is so much exposed wire that you’re practically guaranteed to short something.
Do remember to use electrical tape / hot glue to cover that area afterwards as these will insulate.