There is an old saying - it works better when you plug it in.
I guess my comment about NOT running ANY code and then adjusting the pot did not sink in.
Just connect the + and grounds to BOTH LCD supply and backlight LED and do you intensity adjustment after
the device goes thru its power-on sequence - automatically.
.
It is possible that your is also controlling the backlight so you are better off not running code until you have working hardware.
Not to worry about how much power you drawing - these LCD been around for few yeas and are not that
hungry by itself - its the backlight LED that takes few mA.