test.c

long next_state_change = 0;
long state = -1;

void loop() {
  
  if(digitalRead(PIN_BUTTON) == LOW) {
    state = 5;
    // it will start counting after releasing button
    next_state_change = millis() + 10000;
  }
  else if (millis() >= next_state_change) {
    if (state == 5) {
      state = 0;
    }
    else {
      state = (state + 1) % 4;
    }
    next_state_change = millis() + 1500;
  }

  switch(state) {
    case 0:
      // ....
  }
}