LCD lights up without working

No, it means it lights up.

Can you make the screen go between totally blank to just showing black boxes wheee characters shoukd go by using the contrast potentiometer?

Please post the sketch you are using.

Please draw a schematic diagram, which will be unambiguous. Using a pencil is fine, and so are blocks representing the Arduino and the LCD.

Be sure to show where power is coming from, and how it is routed to the parts that need power.

a7