Hi 
I really don’t understand your code, with comments it would be more readable.
I create a pen in codepen:
// http://codepen.io/erretres/pen/GqLZvW
I don’t understand (the problem), when I click the button “Let’s begin!” change to “Start Room” (document.getElementById() is working, is changing the text:)
document.getElementById("dialogue").innerHTML = "Start Room";
The rest of the code:
var answer;
var room;
var shield;
function start(){
console.log ("startroom");
answer = prompt("You are in a room with a door to the north and a door to the south. Which way do you want to go?");
document.getElementById("dialogue").innerHTML = "Start Room";
if (answer === "go north"){
document.getElementById("dialogue").innerHTML = "Dragon Room";
dragon();
} else if (answer === "go west"){
document.getElementById("dialogue").innerHTML = "west Room";
west();
} else if (answer === "go east"){
answer = prompt("you can't go east. Which way do you want to go?");
} else if (answer === "go south"){
answer = prompt("you can't go south. Which way do you want to go?");
} else if (answer === "quit") {
document.getElementById('dialogue').innerHTML = "bye!";
return;
} else {
answer = prompt("Please choose from available answers. Which way do you want to go?");
}
}
function dragon(){
console.log ("dragon room");
answer = prompt("There is a dragon here. What do you want to do?");
if (answer === "quit");
document.getElementById("dialogue").innerHTML = "Too late, you were eaten.";
return;
}
function west() {
console.log ("westroom");
document.getElementById("dialogue").innerHTML = "west Room";
answer = prompt("You are in a room with a shield. What do you want to do?");
}
$(document).ready(function(){
$("#begin").click(function(){
start();
});
});