My initial test of my multiple display set up resulted in disaster: Don't hook up your ULN2003 with reverse voltage! Now it just spits out random oscillations on its outputs and such resulting in only one line lighting up. I might also not be understanding how my shiftOut() is working, the order of the bits and such.

More tomorrow when I can get a new uln2003...

Here is my code in case it seems like I am missing anything there?

//Pin connected to ST_CP of 74HC595
int latchPin = 8;
//Pin connected to SH_CP of 74HC595
int clockPin = 12;
////Pin connected to DS of 74HC595
int dataPin = 11;
int ledPin = 13;
byte firstByte[] = { 8, 16, 8,16,8,16, 8, 16};
byte secondByte[] = { 255, 255, 255,255,255,255, 255, 255};
byte thirdByte[] = { 255, 255, 255,255,255,255, 255, 255};
byte fourthByte[] = { 8,8,8,8,8,8,8,8};

// { 0,0,0,0,0,0,0,0 }

int sensorPin = A7;    // select the input pin for the potentiometer

int sensorValue = 0;  // variable to store the value coming from the sensor


void setup() {
  //set pins to output so you can control the shift register
  pinMode(latchPin, OUTPUT);
  pinMode(clockPin, OUTPUT);
  pinMode(dataPin, OUTPUT);
  pinMode(ledPin, OUTPUT);
  Serial.begin(9600);
}

void loop() {
  
  digitalWrite(ledPin, LOW);
    
    for (int i=0 ; i < 8 ; i++){
      digitalWrite(ledPin, LOW);
      sensorValue = analogRead(sensorPin);
      /*
      Serial.print(F("i"));
    Serial.println(i);
    Serial.print(F("First Byte"));
    Serial.println(firstByte[i]);
    Serial.print(F("Second Byte"));
    Serial.println(secondByte[i]);
    */
    digitalWrite(latchPin, LOW);
    // shift out the bits:
    shiftOut(dataPin, clockPin, MSBFIRST, firstByte[i]);  
    shiftOut(dataPin, clockPin, MSBFIRST, secondByte[i]);
  shiftOut(dataPin, clockPin, MSBFIRST, thirdByte[i]);
shiftOut(dataPin, clockPin, MSBFIRST, fourthByte[i]);  

    //take the latch pin high so the LEDs will light up:
    digitalWrite(latchPin, HIGH);
    // pause before next value:
    delay(sensorValue);
    //digitalWrite(ledPin, HIGH);
    /*
    digitalWrite(ledPin, HIGH);
    delay(0.001);
    */
    }
    
}