2003 Nissan Maxima engine cuts out

My battery went bad and had car towed home, changed out battery and fired up the car when I went to take off the engine cut out and when I let up on gas pedal it would run smooth, after trying to wiggle connectors and unhooking and re hooking battery nothing, then when I turned on the a/c car ran ok. After test driving I found if I used a lot of power acc.(A/c fan on high, lights on car would run great shut off lights car would start to stall turn off a/c car would cut out completely until I turn a/c and fan back to high, seems like if a lot of power was used car ran fine>