2004 Chevy Trailblazer

Try this, Engine may stall with the air-conditioner on and or while adding additional loads to the engine at idle. An example of an addition load would be turning the steering wheel left or right with the air-conditioning on. This type of stall usually occurs during idle or slow parking lot maneuvers. This concern may not set any diagnostic trouble codes.

Recommendation/Instructions:
Clean the throttle body bore and the throttle valve plate using a clean shop towel with GM top engine cleaner, GM P/N 105262. If the throttle body was dirty, when you replaced the battery it relearned the idle at that position opening the throttle a little more letting more air in which will cause it to stall. Try cleaning the throttle and drive it. Post back if this fixes it.