I think I accidentally changed the dip settings in my Harbor Breeze remote when I changed the battery.
How do I find the correct dip settings? Preferably without opening up the ceiling fan itself.
Thank you!

The only ways are to check the dip switches in/on the fan, or to just use trial and error until it works.

http://www.ceiling-fans-n-more.com/c...e-controls.php

The DIP switches for the fan are not in the fan housing. They are on the receiver on underneath the ceiling mount cover. On my Harbor Breeze fan you slide out the receiver from the ceiling mount - it's a black plastic box - and the DIP switches are there.