Troubleshooting 16x4 LCD Display Showing No Output
The display might need negative panel voltage, especially if the display is large. Your pot now has three pins: the center pin goes to pin 3 and the two other pins go to VCC and GND. Instead of GND, connect that pin to something like -10V. If your board has an RS-232 level shifter (MAX232), you can get the negative voltage from there. Then adjust the potentiometer and see if you get dark squares.

For quick testing, you can also get the negative supply from a lab power supply or a 9 volt battery.