I too just had this Issue...
2016 TC XLT
My battery died (MOTOCRAFT OEM) and leaked all over, then after I painstakingly put in a new battery into that stupid clip front box, the a/c and heat wouldn't work, the damper and vent select wouldn't work either.
The Blower fan and speed selector still works though.
Checked codes with my $70 scan tool, nothing, so I had a shop check codes with their $5000 scan tool... NADA
Continuity checked every fuse in the Van, all were good, no open circuits none shorted either. My TC also had a 7.5A fuse in 71 where a 10A is listed..
Stumped the shop, they think it *may be* the control module, the A/C heat & damper are likely not a strait through connection whereas the Blower probably is.
The only conclusion I can think of is the Battery was at 8-11v before I swapped it out. The temp selector had been left on MAX/AC so maybe the under-voltage shorted the controls out..!?
I REFUSE to go to FORD dealership to diagnose it...
Those limey bast*rds would probably charge me more than a I'd spend on 4 trips to Colorado just to tell me to replace fuse block or add Blinker Fluid.