Depending on the controller type that is on the module you may not see the black squares until the initialisation has been completed. The classic HD44780 always showed squares when the power was OK, but some newer clones don't. Vendors are known to sell the same display with different controllers. Can you take a picture or check the controller type on the LCD? There also seem to be some jumpers on the PC1604A that select either internal or external contrast control. Can you post a picture of the module to check that? This could be a display that actually needs a negative voltage to show sufficient contrast. I now found the specsheet and it says V0 range is between +2 and -6V. Try 0V and see what happens. Could it be that your display only shows visible characters when the backlight is on. Transmissive types are almost invisible without backlight.

EDIT: i have been digging around in my LCD collection and found a powertip PC1602 with an ST7066 controller. The display is similar to your type and it does indeed require a negative contrast voltage (about -1.5 volt) before it shows anything. The controller displays the normal row of square blocks even without actual programming. So you need to provide a small negative voltage either by adding a separate powersupply (1.5V battery?) or by adding a DC/DC converter that uses the positive supply to generate a negative bias. Make sure to remove the negative voltage before removing the powersupply to the LCD to avoid damage.

Thank you Wim, the display started tot show text with V0 at -1.30v, i Fed the circuit via an external power supply. I read my specsheet again, but it was still not clear to me. Can you point to the specsheet your found? Once again thank you for the support! Btw i dont know how to attach files, first time on a forum :-)

The contrast voltage depends on the type of Liquid Crystal material that is being used for the display, it does not depend on the controller type. Obviously the controller has a certain range of voltages that it can withstand, but as long as you stay within its specs there will not be a problem. You will see that LCDs suitable for an extended temperature range often use larger and/or negative contrast voltages. The same is true for displays that have higher refresh frequencies, such as graphics displays. The contrast voltage is normally given or referenced against the positive powersupply (so NOT with reference to GND). The spec sheet for the display says :

LCD Driving Supply voltage Vdd - Vee (so referenced against powersupply Vdd, which is 5V): -0.3...13V That translates to 5V-0.3V = 4.7V down to 5V-13V= -8V (now referenced against GND).

The typical LCD operation voltage for this display is given as 4.2..6.4V. This is again relative to Vdd so 0.8V..-1.4V relative to GND.

The optimal setting for the contrast voltage depends on the ambient temperature and the viewing angle.