I'm having difficulties deciphering just what you wrote in your code, but here's an example of what should roughly happen (in a mixture of C and pseudo code) assuming your circuit is correct.
const int buttonPin = 2;
const int LEDPins[6] = {3, 4, 5, 6, 7, 8};
void setup()
{
pinMode(buttonPin, INPUT);
for (int i = 0; i < 6; i++)
pinMode(LEDPins[i], OUTPUT);
}
void loop()
{
if (digitalRead(buttonPin) == HIGH)
{
for (int i = 0; i < 6; i++)
digitalWrite(LEDPins[i], LOW);
timerRestart(); //pseudo
delay(50); //short delay for debounce
}
if (yourTimerIsOver) //pseudo
{
digitalWriteNextLED //pseudo
}
}
And I would also suggest checking for the tilt sensor with nass' description.