originals
(but after seeing what you guys have done I'll get a pair of replicas to customize)
if the fabric isn't too damaged and you are able to get them clean enough, i'm pretty sure you could dismantle them carefully, but you will need someone with electronic experience to look at the circuit Nike designed.
The 2011 originals have a custom designed PCB board probably, with custom lithium battery and custom wiring.
It will be totallly different to the way we are doing it with these replicas.
But i'm pretty sure you could repair your originals if you contact someone who can understand the pcb board which Nike have used.
if everything is behind that white ankle piece along with the charge pin, then may it be a case of unglueing it, and then working out what has shorted out.
the ankle bubble leds are protected and the sole EL panels are protected with the clear rubber.
So it could be something has damaged the PCB (which i assume is in the white ankle buckle where the charging pin is located).
I doubt the wiring could get damaged, since its tucked away inside the grey fabric somewhere.
I don't think anyone on the web has really dismantled a pair of the real 2011 shoes yet, but it would be interesting to see what they actually did in their design.