Programming not working / serial interfacing not working

int PushButton1 = 0;        //inital value of push button 1 is set to zero
if (PushButton1 == 1) {         //press push button1

Well, that's a pretty silly test, don't you think?

DC = pow(1.5864,PushButton1)-1; //formula for duty cycle

1.58640 is what?

for (int PushButton1=0; PushButton1 <= 10; PushButton1++){        //condition for LED with Button1

This is my brother Darryl and my other brother Darryl. Why do you now have two variables named PushButton1?

  Serial.println("Button1 is Pressed");  //Print to serial port

That would be a lie, because the condition which this statement is executed has NOTHING to do with the state of any switch or pin.