Debugging modified BlinkWithoutDelay
Since it's blink without delay, the next loop will happen immediately. Not after the blink function is don't. So loopCount will increment continuously. You don't limit loopCount to 9, so it will after a few milliseconds try to access, e.g. values[12] which doesn't exist. (see @jfpoilpret's comment)

// constants won't change. Used here to set a pin number :
const int ledPin =  13;      // the number of the LED pin

// Variables will change :
int ledState = LOW;             // ledState used to set the LED

// Generally, you should use "unsigned long" for variables that hold time
// The value will quickly become too large for an int to store
unsigned long previousMillis = 0;        // will store last time LED was updated
int blinkValues[] = {1000, 1000, 1000, 200, 200, 200, 1000, 1000, 100};
int loopCount = 0;


// constants won't change :
//unsigned long interval = 1000;           // interval at which to blink (milliseconds)

// Number of times to blink
const long blinkMax = 10;
// Counter for number of times blinked
unsigned long blinkCount = 0;

void setup() {
  // set the digital pin as output:
  pinMode(ledPin, OUTPUT);
}

void loop()
{
  blink();
}

void blink()
{
  unsigned long currentMillis = millis();
  if(currentMillis - previousMillis &gt;= blinkValues[loopCount]) {
    previousMillis = currentMillis;   
    loopCount = (loopCount + 1) % 9;
    if (ledState == LOW)
      ledState = HIGH;
    else
      ledState = LOW;
    digitalWrite(ledPin, ledState);
  }
}


Also note that the blink function will toggle the led, after the interval. So you need to add intervals, for how long the led should be off between flashes. But I leave that for you to figure out.