An LCD will show blocks like that if it isn't initialized correctly. You may have an intermittently-bad connection on one or more of the control lines.

To avoid intermittent connections, you could use a shield with soldered pins, or could get multipin shells to replace the single-pin shells of the Dupont-type connectors shown in the photograph. Having adjacent connectors fixed in a single multipin shell results in more-stable connections.

An LCD will show blocks like that if it isn't initialized correctly. You may have an intermittently-bad connection on one or more of the control lines. [But see edit 1, below, regarding contrast adjustment.]

To avoid intermittent connections, you could use a shield with soldered pins, or could get multipin shells to replace the single-pin shells of the Dupont-type connectors shown in the photograph. Having adjacent connectors fixed in a single multipin shell results in more-stable connections.

Edit 1: As noted in a comment, blocks appearing on both lines is typical of contrast adjustment problems or missing contrast voltage. On the other hand, blocks appearing on just the first line is typical of incorrect initialization, which could be caused by poor connections or by software errors.

Below is a sketch that repeatedly initializes the LCD and then displays different sets of characters for a few seconds each.

Note, if you don't have the Streaming.h contributed library installed, you can get Streaming5.zip from arduiniana.org.

Note, if not using an I2C-interfaced LCD, change the included LCD library .h from LiquidCrystal_I2C.h to whatever is appropriate, and remove I2C-address-related stuff from the sketch. If you are using an I2C-interfaced LCD on a known fixed address, remove the lcd.setAddress(address); and lcd.getAddress(address); stuff. Those routines are not part of the usual LCD libraries; they probably can be added by subclassing LiquidCrystal_I2C, but on my system I added code as shown after the sketch.

/* Screen-test sketch for PCF8574/PCF8574A/PCF8574T I2C LCD Backpack 
Uses library from https://bitbucket.org/fmalpartida/new-liquidcrystal/downloads GNU General Public License, version 3 (GPL-3.0) */
#include <Streaming.h>
#include <Wire.h>
#include <LCD.h>
#include <LiquidCrystal_I2C.h>

enum { LCDcols=16, LCDrows=2 };        // # of rows and cols on LCD
enum { LCDaddr2=0x27, LCDaddr3=0x3F}; // For TI PCF8754 or PCF8754A 
LiquidCrystal_I2C lcd(LCDaddr2,2,1,0,4,5,6,7);

void initLCD(byte address) {
  byte cdata[8];
  Serial << "initLCD(" << _HEX(address) << ')' << endl;
  lcd.setAddress(address);       // Set LCD I2C address
  Serial << "LCD address ... " << _HEX(lcd.getAddress()) << endl;
  // activate LCD module
  lcd.begin(LCDcols, LCDrows);
  lcd.setBacklightPin(3,POSITIVE);
  lcd.setBacklight(HIGH);
  lcd.noCursor();

  // Load custom characters
  for (int c=0; c<8; ++c) {
    unsigned int d = ((c+4)<<12 | (c|3)<<9 | (c|2)<<6 | (c|1)<<3 | c) ^ 0x5555;
    //Serial << "c=" << c << "  d=" << _HEX(d) << endl;
    for (byte k=0; k<8; ++k)
      cdata[k] = d >> k;
    lcd.createChar(c, cdata);
  }
  lcd.home ();
  lcd.print("Initialized");
  delay(1000);
}

void setup() {
  Serial.begin(115200);
  Serial << "Starting up" << endl;
  Wire.begin();                 // Setup to wirescan to check for 8754 addr
  Serial << "after Wire.begin()" << endl;
  TWBR = 152;  // 50 kHz, use if it works, or use slower rate
  TWBR = 158;  // 12.5 kHz, = slower rate 
  TWSR |= bit (TWPS0);  // change prescaler
  Serial << "after TWBR / TWSR" << endl;
  Wire.beginTransmission (LCDaddr2);
  Serial << "after Wire.beginTransmission()" << endl;
  if (Wire.endTransmission() == 0) // Does 0x27 succeed?
    initLCD(LCDaddr2);          // Set up with 0x27 address
  else
    initLCD(LCDaddr3);          // Set up with 0x3F address
  Serial << "after initLCD()" << endl;
}

void show(char base, byte delt) {
  enum {MD=2000};
  byte k, ro;
  for (ro=0; ro<LCDrows; ++ro) {
    lcd.setCursor(0, ro);
    for (k=0; k<LCDcols; ++k) {
      lcd.print(base);
      base += delt;
    }
  }
  if (base==' ') {
    lcd.setCursor(1, 1);
    lcd << "LCD @" << _HEX(lcd.getAddress()) << " =" << lcd.getAddress();
  }
  delay(MD);
}

long p=0;
void loop() {
  byte c;
  Serial << "Pass " << p++ << " on " << _HEX(lcd.getAddress()) << " at t=" << millis() << endl;
  lcd.home ();          // Set cursor to 0,0
  show('#', 0);         // Screen of # characters
  show(' ', 0);         // Screen of ' ' characters
  show('@', 0);         // Screen of @ characters
  show( 0,  1);         // lo specials + ' '...'/'
  for (c=' '; c < '~'; c+=16)
    show(c, 1);

  lcd.setBacklight(HIGH);
  while (Serial.available()) {
    c = Serial.read();
    if (c == '2') initLCD(LCDaddr2);
    if (c == '3') initLCD(LCDaddr3);
  }
}

To add lcd.setAddress(address); and lcd.getAddress(address); routines:

// add after void setBacklight(...); in LiquidCrystal_I2C.h
void setAddress(uint8_t addr);
uint8_t getAddress();

and

// add after void setBacklight(...); in LiquidCrystal_I2C.cpp
void LiquidCrystal_I2C::setAddress(uint8_t addr) {
  LiquidCrystal_I2C::_Addr = addr;
}
uint8_t LiquidCrystal_I2C::getAddress() {
  return LiquidCrystal_I2C::_Addr;
}