sorry about the image, my photoshop on my net book has been giving me issues lately so i've tried to modify some stuff within it that is causing it to only allow me to save to web, and on the netbook the window is off the screen so i only can do gif at the moment...
on a note, i would start by re-soldering these connections, what wattage is your soldering iron? it looks like it is HELLA HOT (based on melted connector)
another thing to check, which i cant see based on the image is if any of the solder is grounding out. i would clean the joints after you are done to check for that (use a q-tip and some alcohol if you dont have anything better)
hope that helps
(not familiar with 360 controller much, so I'm not sure of the pin-outs based on the picture and location of chips)