Most likely it is the resistor. It's located behind the glove box on the evaporative housing. You should also check the ohm draw on the fan. It may be failing which will cause the resistor to fail. I've found most resistors to fail at about 125k miles regardless of fan condition, though.
I have a 2001 Town and Country and the same thing happened to me. It has a front blower control unit/module under the dash on the passenger side. It has a large aluminum finned heat sink on it. The control cost me $75 at my local Dodge Dealer parts counter. It had a couple of screws and plug-in connections so I changed it myself.