if it has automatic climate control which iirc the 172 has, it doesnt have a resistor pack. The thing that is bolted inline from the motor air outlet with the silver heatsink sticking out of the bottom of it is an electronic dc motor controller. Its just over £100 for a new one from a dealer. I wasnt going to pay that so i repaired it myself for under £20. ive repaired a few since then and its always been the same componet that has failed. Ive always replaced it with an uprated one and never had any faults come back.
If you want anymore help and think it is that, that has failed drop me a pm