The fan speed is inoperable at the higher settings above what's selected in the image. Any suggestions on what to check myself before taking to the dealer?

 

What fan speed works when you push the MAX button?

If you get high speed on the blower that way it may isolate the problem to the rotary switch and not the motor or other controllers/computers. I hope it's something simple for your sake!

 

I'm guessing a battery problem.

I had exactly similar problem and I changed to a new battery and it was solved. These cars can act weird with a bad battery.
Try charging your batt or try with another.

- Antti -

 

Replacing the battery will help to 100%. Do not forget to register a new battery.