What do you mean by this - the Atmel ATMega 328P?
I think you are looking at two separate problems.
But first, you say you have two units and both show exactly the same faults? That strongly suggests to me that there’s a problem either with your interpretation of the build instructions (and you copied your earlier mistake) or you have a bad sketch or software library. Or it’s quite possible that you have both.
First, I suggest you reinstall/update the relevant libraries. Note that it’s not sufficient to rename the old ones, if you want to keep copies, zip them and then delete all copies of the library.
The backlight. This is very simply an LED that’s driven by a PWM output pin. To test it, you can use what is little more than a one-line sketch. This should turn the backlight on for 5 s, then off for 5 s.
#include "Arduino.h"
#define BACKLIGHT 3
void setup() {
pinMode(BACKLIGHT, OUTPUT);
digitalWrite(BACKLIGHT, HIGH);
}
void loop()
{
delay(5000);
digitalWrite(BACKLIGHT, LOW);
delay(5000);
digitalWrite(BACKLIGHT, HIGH);
}
If the backlight does not light, check the voltage across the LED wires (~ 2.8 V) and at the IRQ pad on the PCB (~ 3.2 V).
If the backlight lights, then, because in the Tester sketch it’s driven via the GLCD library, this plus the other symptoms are a strong (but not conclusive) argument for a problem with that library or its installation.
[Edit]
Can we have a sharp clear photo of the PCB (component side) to check your component placement?