Had the same problem recently on my 2011 EXP-KR.
Huge build up of deposits that didnt allow the vehicle to crank. Found the positive terminal broken. Temporarily cleaned with hot water and given a scrub with fine sand paper and then greased to stop the air from touching the terminal and re-forming the deposits. So far so good as a temporary measure.
Meanwhile, tried to go out to check aftermarket terminals, but although plenty chinese ones available, nothing that can be directly replaced nice and easy. I need to un-crimp one of the cables from the positive terminal, and the other cable is lugged, wont fit into the aftermarket terminals which come with a wing nut.
Being a lazy guy not willing to re-lug the cable or un-crimp the other while outdoor temperatures touch 45 deg C (Not helped by the fact that Mr Ford has given me a cable that barely reached the terminal, and any change would reduce the cable length that would make me have to replace the entire starter cable), i
found that while Ford sells the complete starter cable with the terminal attached for the EXP, they sell the terminal separately for the FORD Edge, the part number of which is BT4Z-14450-AA and BA for the positive and negative terminals respectively. Selling online on Amazon, Ebay and parts.com which was the cheapest.
This terminal is an exact replacement for my 2011 EXP as well as for F150 of various years. Check if it fits the 2016 EXP as well.
ps. Over 1 phone call I found the local dealership has the positive terminal and is willing to let it go for the fair sum of $12 in Qatari Riyals so i'm off to the dealership this weekend, although, as previously mentioned, being a bit lazy, i will put off the repair till the winter months. (That adds to the front passenger window which needs to be looked at as it refuses to budge, open the central console to try and fix the head unit that collapsed into the dashboard void due to the support structure breaking, probably due to heat, and a bunch of other things....)