When initializing the LCD, the backlight automatically goes of

Doing something wrong then. You might want to use a logic analyzer to review what signalling you're achieving, or interface on another micro-controller directly to GPIO pins to achieve a better understanding or how to control the display.

You might want to consider the use of an I2C OLED 128x64 or 128x32, they are easy to interface and cheap, and less 1990's