I have an S5 also, I haven't had this problem. I have extra batteries along with an external wall charger.
I use the wall charger to avoid charging my phone. It was $15 on ebay, and it may be a viable workaround and/or solution outside of replacing the motherboard.
These wall chargers will charge your battery no matter what, you can confirm this by looking at the pins on the image below. If the third pin not present, the charger does not check battery stats before charging.
(I consider this a solution, because we'll be taking advantage of the removable battery feature, and the chargers come in packs of three batteries so you'll never be stuck to an outlet again. I recommend labeling each battery with lines around the curved edges.)
Anyway, hope this helps.