If I'm not mistaken, the thermostat is 24 volts. I've never turned the power off to the furnace when changing them. The battery only runs the electronic controls in the unit and doesn't get power from the wiring.
I think it has something to do with the wiring in the new thermostat. I would go back and check the wiring instructions. Thermostats are either 3, 4 or 5 wire. Some require that you either remove a "jumper" from one of the posts to another. Some require the installation of a "jumper." Some even require different colors going to different posts on the back of the thermostat. Check the instructions again and confirm it is hooked up correctly.