Can't speak for the '04 directly, but the '03 does not appear to have a fuse other than whatever fuse is on the ignition switch. The current that drives the fan motor will always be limited by the resistor block that determines fan speed, so Dodge must have taken that into account. Seems strange to me not to have it separately fused.
Very simple circuit. The connectors have come loose, a wire has come loose, the fan motor is burned or the resistor block is open. That is pretty much all there is.