Based on your diagram and the datasheet, you have confused where the datasheet lists the LED backlight voltage & current requirements for the LCD module with the yellow/green backlight (which is the part number on your diagram) and the requirements for the module with the white backlight (which are the numbers you quoted in the question).
If you have any doubts about the datasheet, I recommend that you double-check with the manufacturer. However based on the information you provided, I have listed the problems that I found.
Your diagram shows the part number as:
From the datasheet, that G means it is the version with the "Y/G" (yellow/green) colour LED backlight.
I've checked the voltages on VDD (Pin 2) and LED Backlight (Pin 17) and they are getting 3.3V.
However the datasheet says that for the green LED backlight:
Forward voltage for yellow/green backlight is 3.9~4.2V
Therefore one problem is that you are not supplying the correct voltage to the yellow/green backlight.
Also, you have got the current calculation wrong, because the datasheet says:
LED BACKLIGHT Y/G max. 150mA@+25°C
But you were quoting the 45mA LED current for the white LED backlight (which is a different LCD module part number):
The datasheet says the maximum current on LED Backlight pin is 45mA
Therefore if you have listed the correct part number EA DIP203G-4NLED on your diagram, you need a 5V or greater power supply to the LED backlight, and then calculate the series resistor to pin 17 for an appropriate current (I would not aim for the maximum 150mA current, and note that the datasheet mentions de-rating the maximum current above 25°C, although it doesn't give further details). I hope you have a 5V (or greater) power supply, which can supply the necessary current!
For example, with a 5V backlight supply, depending on what resistor values you have available, I would start with around a 20 Ω resistor, aiming for around 50mA current and a 1V drop across the resistor, to give 4V at pin 17 - and tune the value from there, after you see how bright the backlight is.