I had the same problems, bas/esp light and spoiler up when mice chewed the wire under the hood going to the speed sensor and wear indicator. The spoiler is a fail safe because it supposed to hold the rear of the car down above 62 MPH. if the computer is not getting reading from speed sensor the fin goes up.
I also had the same problem along with no crank, tranny limp mode, wear indictor light, brake light and asb light ,and bas/esp lights on dash. Along with no brake lights when pedal pushed. Cured it all with a new relay control module.
If you had none of this prior to battery change I would try the reset of computer first.