Hello and thanks for trusting me to help you today. I am a licensed diagnostic and repair technician, I look forward to working with you.
As this was as a result of the battery being replaced I think its safe to say the fault is not actually with the parking brake. I think one of two things have happened, either the control unit for the parking brake has suffered for a bit of a glitch as the battery was reconnected (this is common due to the voltage spike that can occur) Or worst case, its caused internal damage to the control unit, this tends to happen if the battery terminal is not connected in one hit, and is touched on and off several times.
Naturally being all electronic your are limited to what you can do without plugging it into a diagnostic system to see whats going on, but if there is a glitch, it may be cured by re-setting the control units, however it may need calibrating if its lost its memory which again needs to be plugged in to do.To reset the control unit your self, simply disconnect the negative terminal of the battery for 5 mins then reconnect the battery. This will do a basic reset and often will cure a lot of random problems like this.
That would point to a problem with a control unit, I would try to reset everything as i mentioned above to see what happens then, if its not returned back to normal i suspect it may have damaged the ECU