Interesting, I have had a little bit of experience with giving devices... a little bit too much juice.
My first steps would be:
1) Find the exact model number of the Kinect (usually written on it)
2) Find a Schematic for this model so you know what you are looking at.
3) Open it up
4) Follow the power line in from the USB and check for damage.
If its power in general, a good designer would put some sort of over power protection into the circuit, this could be some sort of Power control chip or Diode, a Fuse of some kind or maybe it is part of the USB controller chip.
Make educated guesses on the components that are in line and see if you can replace or Identify the fault as you follow the power deeper into the device.