With Andrew Thompson's help I was able to solve my issue. First of all, I had to use the example that used a codebase.
Here is my manifest file:
Permissions: sandbox
**Codebase: localhost:8080/java-web-start**
Application-Name: Dynamic Tree Demo
Here is my jnlp file:
Dynamic Tree Demo
Dynamic Team
</resources>
<application-desc
name="Dynamic Tree Demo Application"
main-class="webstartComponentArch.DynamicTreeApplication">
</application-desc>
<update check="background"/>
</jnlp>
And the HTML file:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html lang="en-US">
<head>
<title>Dynamic Tree Java Web Start Application Page</title>
<meta http-equiv="Content-Type" content="text/html; charset=windows-1252">
</head>
<body>
<h1>Dynamic Tree Java Web Start Application Demo</h1>
<script src="https://www.java.com/js/deployJava.js"></script>
<script>
var url = "**http://localhost:8080/java-web-start/dynamictree_webstart.jnlp**";
deployJava.createWebStartLaunchButton(url, '1.6.0');
</script>
<noscript>JavaScript is required for this page.</noscript>
</body>
</html>