Take a picture of the LCD (without flash) with the pot. at full clockwise and full counter clockwise. In one extreme the LCD will be blank at the other it will have a matrix of character size black blocks. If you do not get this go no further. something is wrong.
When I use one of these displays I solder a 1x16 male header to bottom of LCD and then plug LCD into solderless breadboard. Then using solid wire add pot and wires to Arduino. That way I know all connections are good.