Mine did the exact same thing. What I've had to replace is the fan control switch, not very expensive from local dealer. Is your knob ok?
seriously, my knobs that go to the switches wore out so it would turn, but the switch itself would not turn because the knob was rotating on the shaft. easy check is to pull them off and swap them around.
The AC/Heat control switch could have a bad connection. When I pulled mine apart, the connector to it was melted. I was able to repair it once fairly easy, the second time I had to completely remove the melted connector and mod it up.
The resistors as stated above is a common problem with Jeeps but I've not had to replace mine yet.