unsigned long previousMillis = 0;        // will store last time LED was updated
const long interval = 500;           // interval at which to blink (milliseconds)
const int led = 12;      // the number of the LED pin
int ledState = HIGH;             // ledState used to set the LED
boolean state = false;

void setup() {
  Serial.begin(9600);
  pinMode(led, OUTPUT);
  digitalWrite(led, HIGH);
  for (int thisPin = 12; thisPin < 12; thisPin++) {
    pinMode(thisPin, OUTPUT);
  }
}

void loop() {
  if (Serial.available()) {
    int serialinput = Serial.read();
    switch (serialinput) {
      // Your existing case statements...
      case 'a':
        digitalWrite(led, HIGH);
        state = true;
        break;
      case 'b':
        Serial.print("NUMBER 2");
        Serial.println(" ");
        break;
      case 'c':
        Serial.print("NUMBER 3");
        Serial.println(" ");
        break;
      default:
        for (int thisPin = 12; thisPin < 12; thisPin++) {
          digitalWrite(thisPin, HIGH);
        }
    }
  }
  if (state == true) {
    Blink();
  } else {
    digitalWrite(led, HIGH); // check to make sure it's off incase it was still on
  }
}

void Blink() {
  unsigned long currentMillis = millis();
  if (currentMillis - previousMillis >= interval) {
    previousMillis = currentMillis;
    if (ledState == HIGH) {
      ledState = LOW;
    } else {
      ledState = HIGH;
    }
    digitalWrite(led, ledState);
  }
}