I take no responsibility for what happens to your intercooler if you attempt to do any of the things mentioned in this post. Since I do not have one of my own to look at, these are speculations
And do remember, ground yourself, WEAR GLOVES, all the safety precautions. If you hear squeaking noises at any time stop what you're doing and unplug whatever is connected to power.
First take the circuit board out and see if you notice any microchips on it. If not, then try placing a paper clip or a strand of wire across the two globs of solder where the red wires attach to the circuit board while the cooler is plugged into a power source to see if that does anything. If it runs, you're in business. All you need to do is bridge the two points with a wire and some solder.
If that didn't work then your other option is to splice the wires from the power source to the fans directly. This is what I've done for my own xbox with an old power adapter and a couple of computer fans. You'll need some electrical tape for this. Take the circuit board out; you won't need it anymore. Cut the white wires, taking care to leave as much possible attached to the fans. Then take your power adapter and cut the connector that goes to the nyko. Strip some of the insulation to expose the two wires.
Very Important. You must take care that these two wires never touch or connect in any way while the adapter is plugged in. If you hear the squeaking noise or the wires start to glow, separate them immediately. In fact, keep the adapter unplugged while you solder.
Wrap a little piece of electrical tape around one of the wires (on the insulation, not the metal part) to mark it and differentiate it from the other wire. Plug your adapter in (remember not to let the wires touch). Now take a white wire from a single fan, and touch it to the marked wire while you touch the fan's other white wire to the other wire from the power adapter. If it spins the right way, mark the white wire that touched the adapter wire with electrical tape on it with some electrical tape of its own. If it doesn't spin, switch the wires around. Repeat this test for the other fan(s). Unplug your adapter.
Now all that remains is to solder all the wires marked with electrical tape together and the same for the unmarked ones. After you're done, COVER ALL EXPOSED WIRE WITH ELECTRICAL TAPE. I'll leave it up to you on how you route the wires out of the case. You may want to drill some holes in the side of the case.
You can also do what I did and find an old 12v adapter and hack it up in this same style and attach it to two computer fans, provided the adapter can supply enough amperage. The fans will fit PERFECTLY between the power connector and the video connector so you don't have to do anything special.
Youtube has some guides on soldering. It's not that hard once you get the hang of it.