Cory, do these cars have a Blower Relay as well? I have seen them go on other vehicles. Rare to find it bad and a blown resistor pack but it can happen.
Side note: Not uncommon for an older blower fan to start taking out the resistor packs by the drawing more power than new motor does. If you start replacing the packs every year or less then look into the fan motors amp draw and see if it is exceeding the factory specified amp draw, if so then replace it as well.
Usually when the resistor goes out, the blower still works, just only on one speed. Had that problem with a Lincoln, and I see it all day at the parts store. When the blower itself goes bad, there will be zero activity from the blower. Take it out and use some gator clips to temporarally straight-wire it to the battery. You'll only have to touch it for a nanosecond to see if the fan cuts on. If it does, your problem is elsewhere. But I think it wont.
I don't know if they have a relay. A lot of times when the resistor pack on these goes bad, the blower motor won't shut off. But that is not always the case. It could be a bad head unit as well. But, I would agree, and put my money on the blower motor.