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Yeah those things look torn out. You should still be able to get it working though after doing some trace repairs with jumper wires. I would use 30awg wire for the repairs. Red will fix the VCC rail (AN+) power to the Sticks, TP103 to both marked spots. Blue will fix the Y-axis, top side of R50 to marked spot. Green will fix the X-axis, marked spot to bottom side of R34 on top of the board. You could also just run the wire from R34 thru the hole there instead, as long as it is small enough so it and the Stick lead fit.Yellow will fix LSC, TP106 to marked spot.
Gotcha on the lead bending now.Your last pic, the 3 little posts in the corners there keep the POT fixed to the metal housing in one position. You cut all 3 of those off flush. Do not cut the 2 larger tabs, as they are what hold the POT onto the metal Stick housing. With those 3 posts cut, when you clip the POT back onto the housing , it's free to rotate (albeit slightly as the tabs only let it move so far) but it usually doesn't take much rotation at all to correct one. Then solder it in place and you're good to go.What happens when you do that is you are changing where the Wiper sits for the center position. It's the same thing as if you just barely moved the Stick itself a hair with your thumb to the correct center spot, but you obviously can't hold it there all the time, so you''re rotating the POT instead of moving the Stick to get things centered back up in there.