Yay! It works now. However, when I start it (and restart it) I am greeted with a high pitches buzz and keeps the LED on until I press enter. I think there is an easy fix for this, though.
I feel like such an idiot.
EDIT: Found a fix. It seems that after a pins type is declared, it sets it to high (for OUTPUTS). So I made it so once setup is complete, it sets them to LOW.
void setup() {
pinMode(53, INPUT); //DIP posistion 1
pinMode(51, INPUT); //DIP position 2
pinMode(49, INPUT); //DIP position 3
pinMode(47, INPUT); //DIP position 4
pinMode(45, INPUT); //DIP position 5
pinMode(52, OUTPUT); //Piezo Buzzer
pinMode(50, OUTPUT); //LED
pinMode(48, INPUT); //"enter" button
digitalWrite(50, LOW);
digitalWrite(52, LOW);
}