If you do not hear the motor rpm increase as throttle going up it might be a calibration problem of the esc , check also in your logs if your throttle pwm output at max is around 2000 if not check your radio setup and do a new radio calibration in Mission Planner.
LiOn battery typically have very low C rating. Based on your info, at best your pack is 6C at best. Wouldn’t surprise me if your setup is pulling 15+C to lift 4kg.
Are you sure it’s 20A and not 2.0A or 2000mAh? A car battery is 85A (just for comparison).
A quick plug into eCalc shows your setup has 1.4 thrust-weight ratio with 68% throttle to hover at 64amp draw. Have you tried using a LiPo battery instead?
20A is not the “normal” current it is the VERY max current the battery can hold for a little time and if you translate that in C terms , it is just 6,66C of discharge .
But at 20A that battery will become VERY hot and will provide energy just for 6 minutes not the expected 9 minutes. Consider also that with high discharge rate the tension will be quite low.
If you tell me your AUW and the prop diameter I can tell you more