I have a 2012 limited edition fx35, which I LOVE. Just took it in last week has gauge was reading empty and digital reading at 0 miles on an almost full tank. Your battery may have just been a kawinkadink. Turned out to be a spring of some sort related to the fuel reading, whether it was a middle or float I'm not sure. Do know it was a spring that was replaced. Was covered by warranty and even if it would've been out of warranty they would've fixed it at a dealership. Evidently been an issue since the Fx rolled off the line.