First test the controller now that the Stick is removed. The L3 should not be pressed at all. If it still acts pressed all the time, then something is really messed up and is holding the L3 button line Hi. The torn up trace spot on the right is of no real concern, it's just for the solder lug of the Stick. The one on the left is the 3.2v for the L3 common, you can just jumper wire over from either of the Stick POTs 3.2v after it's reinstalled to get that connection restored. It is not causing the L3 pressed all the time issue, there's either something else doing that or the button in that Stick is stuck in the closed position.