that fan might be thermally controlled, so once the PSU heats up it kicks on. If not what you can do is open up the PSU (unplug it for at least 30 seconds beforehand), and connect the red wire of the fan straight to the 12v rail. This will make the fan run at full tilt though so it might be loud if you do that. If it would keep it cool enough you could hook up the wire to the 5v rail.
This of course is assuming that the fan isn't dead.
If the PSU is under warranty still use it, opening the PSU will void the warranty.