Yes you are correct the one in the dash ,with buttons EATC, This the brain of the a/c system .
If you know a shop with a good tech & scanner , I would scan first , instead throwing parts at it of course, but in case, no scan available then buy the eatc on Ebay, ( will be the cheapest) and you can find them new oem brand just like the one at your local dealer .
let me know what happens, cause if you do get the codes , I will help you with it .
Positive Rating is much Appreciated
This Post will stay Open For You To Come Back And Me Ask Any Follow up Question You May Have On This Issue .
Hope I was helpful to you , please let me know if you need anything else.
Chad ( aka -Customer )