arduino operation game

Please help me I'm trying to build a homemade operation game but I'm having some trouble. I'm trying to make it so when you touch the edge of the hole an LED lights up, a buzzer goes off, plus I'm going to have an LCD that displays how many times you touched the side. I don't have the gameboard yet just prototyping with wires. Here's the code:
int LED = 13;
int kill = 0;
int Buzzer = 9;

void setup() {
// put your setup code here, to run once:
pinMode(2, INPUT);
}

void loop() {
// put your main code here, to run repeatedly:
while(digitalRead(2) == HIGH)
{
digitalWrite(LED, HIGH);
digitalWrite(Buzzer, HIGH)
; kill = kill + 1;
}
}

When I touch the wire in the 5V pin to the wire in pin 2 nothing happens any suggestion?

You forgot to set pin 13 to output. Add pinMode(LED,OUTPUT); in setup.

First of all, I think this is wrong approach.

while(digitalRead(2) == HIGH)
{
  digitalWrite(LED, HIGH);
  digitalWrite(Buzzer, HIGH);
  kill = kill + 1;
}

I believe 'kill' is meant to be amount of times player touched the board. Problem is, in this loop, this variable will be increased very quickly at each iteration if pin is touching the border. The correct solution would be:

  1. Register border's touch;
  2. Ensure player is touching the border for enough time to exclude noise (10 milliseconds or so);
  3. Increase 'kill' by 1 and set some temporary flag, 'isTouching', for example. While this flag is set, no increasing is done.
  4. When (and only when) player stopped touching the border, ensure he is not touching it again for a while (I would put 10 milliseconds again).
  5. Only then clear that flag.

In summary, it should look like this:

int LED = 13;
int Buzzer = 9;
int Touch = 2;

const int necessary_delay=10; //in milliseconds
bool isTouching = false; //Note how it is declared outside the loop
unsigned long countStart;
int kill = 0;


void setup()
{
 /*Not always necessary with some boards with pin 13 automatically connected to led, but shouldn't harm. Also, LED could be changed later. */
 pinMode(LED, OUTPUT); 
 pinMode(Buzzer, OUTPUT);
 pinMode(Touch, INPUT);
}

void loop_touching()
{
 unsigned long m = millis();
 
 digitalWrite(LED, isTouching);
 digitalWrite(Buzzer, isTouching);
 
    if(digitalRead(Touch) == HIGH)
    {
 if(isTouching){countStart=m;return;}
 if(m-countStart >= necessary_delay)
 {
 countStart=m;
 kill++; //once!
 isTouching=true;return;
 }
 }
 else 
 if(digitalRead(Touch)== LOW) {
 if(!isTouching){countStart=m;return;}
 if(m-countStart >= necessary_delay)
 {
 countStart=m;
 isTouching=false;
 return;
 }
 }
}
void loop()
{
  loop_touching();
  // do any other things necessary as in normal loop, 'coz loop_touching does not introduce delays
}