I've gotten a lot of texts/calls/emails recently about the key fob battery. Also, some people have expressed the same thing you have, meaning they change the battery and the light is still there. The only thing I've suggested that's worked is just try changing the battery once more. I've had really good luck with Energizer 2032 batteries for the FOB.
Regarding the CEL, it has nothing to do with the key fob battery, just a strange coincidence. Have it scanned.
Regarding the CEL, it has nothing to do with the key fob battery, just a strange coincidence. Have it scanned.