If that's how you have it wired up then the new button should be working, provided it's a N.O. Momentary type like the original Sync button is.
Check the Sync line and make sure the old button isn't shorted to ground, but does short to ground when pressed. If that works then it's either something on the Sync line (bad via or solder joint at the MCU) or the MCU is bad on that pin.
You should still be able to plug up a PnC cable and force the controller to Sync to the 360, and while that's not a fix for the problem, it's at least a workaround so the controller can still be used. Then if that doesn't work and you're sure the button, trace and MCU solder joint are all good, toss it.