Firstly MPLAB X IDE is a development environment while MPLAB XC8 is a compiler. So you can use MPLAB XC8 compiler with your MPLAB X IDE v3.20.
Seems like you have some connection problems. LCD backlight will work even if the microcontroller program is wrong.
Secondly in that project we are using PIC 16F877A, so that hex file won’t work for PIC 18F4550. So you need make necessary changes in the program and rebuild it for 18F4550.