Although there may be differences between my 1992 XJ and your 2004 grand , this problem your experiencing sounds strikingly similar to a problem I had an recently repaired . I don't believe the wiring in your dash is that much different than my jeep except for the blower motor resister which is of different design . My mom and dad's 2000 and my brothers 1999 use a similar part.
What happened to my '92 and was a problem from the time I got it back in 2001 was the wiring harness behind the dash that runs from the climate control to,the resister and blower motor was shorted due to overheated wiring. Meltdown. This I believe was caused by loose terminals on the blower motor speed switch and corroded blower motor resister causing excessive resistance and running the fan speed on high for heat , defrost or a/c contributes. The dash is a bit involved to remove on you GC but if you can follow the wires from the resister up toward the climate control to inspect for shorts , that will help and with the ignition off you can unplug the resister connection and do an ohm test holding one test lead to one terminal and checking all the other wires if continuity is found which may mean there is continuity due to melted insulation and wires touching. Look for a wiring diagram for the fan and dash circuit as there may be high speed wires from the climate control to resister to motor that will read continuity but are supposed to but powered separately during different speed select. A diagram will confirm. Bundled with these wires were my a/c thermostat wires to low pressure switch and PCM which were shorted as well .
Again , a wiring diagram is your best friend and will help plan a good diagnostic check. Without a good diagram , you would be needlessly taking apart things and wasting time. I did have to remove my dash to repair , hoping you won't have to do the same. Mine was not too difficult but your dash is a bit more involved . It needs to be checked as these parts are VERY expensive as you know and my family has told me about their journeys as well . Wishing you the best of luck .
P.S. - welcome to Jeepz.com and thank you for your membership . Hoping that this post may serve you well and your problem solved soonest.