Arduino LED matrix and 2D array, data seems to be corrupting
Your initial problem can be sorted out by using a longer delay. 

void updateScreen(int screen[8][8]) {

  Serial.begin(9600);
  int i;
  ........
      delay(100); //Longer time duration
      blank();
    digitalWrite(i, HIGH);
  }

}


As far as the chess pattern is concerned, it displays correctly for me.

void loop() {

  int display [8][8] = {
  {1,0,1,0,1,0,1,0},
  {0,1,0,1,0,1,0,1},
  {1,0,1,0,1,0,1,0},
  {0,1,0,1,0,1,0,1},
  {1,0,1,0,1,0,1,0},
  {0,1,0,1,0,1,0,1},
  {1,0,1,0,1,0,1,0},
  {0,1,0,1,0,1,0,1}
  };

  updateScreen(display);
}


Check your array declarations for errors.