I had the dead fan problem with my wife's 1999 QX4 about a year ago. After using this site to track the problem down to the Fan Control AMP module, I disassembled the AMP module and tracked the problem down to the failed component within that package. The component that fails within this module has a custom part number that will not cross reference to a standard replacement component (I think an NEC number on mine if I remember correctly). However, after a little more research, I decided to take an educated guess at what the component was and went with an N-Channel MOSFET.
I replaced the failed component within the metal case (making sure to properly re-heat sink the replacement component since all fan motor current is driven through this small part). You will have to solder the part into place, but there are only three pins on the part, so it's a fairly easy repair. The repaired amp module has worked perfectly fine. We haven't had a problem in over a year now. The replacement component costs about $3.
That takes the repair of this problem from a $700 dealer repair, all the way down to a $3 component replacement if you are willing to get out your soldering iron. Use the directions from another author in this thread to remove the AMP module metal can (The pictorial instructions provided in this thread are excellent). Then open the can and find the only part that looks like the one pictured in the link below.
A link to the replacement part follows:
http://parts.digikey.com/1/par....html
This fix took the $700 dealer repair beyond the savings of going with the $120 module replacement - all the way down to a $3 component replacement.
By the way, there is also a thermal fuse in the module. Mine checked out ok with the ohm meter, but I replaced it also anyways since I had the module opened to replace the MOSFET. The part number I used for that component follows:
http://parts.digikey.com/1/par....html
I hope others can have the same success in savings I had with this repair.