Your "More System Details" doesn't show any Java plugin at all. Are you sure you have the current version installed? This test page will lead you to a download if needed:

http://www.java.com/en/download/testjava.jsp

If you have Java installed, check whether its two plugins (Java Platform SE and Java Deployment Toolkit) are set to "Never Activate" on the Add-ons page. That disables them. Open the Add-ons page using either:

• Ctrl+Shift+a
• orange Firefox button (or Tools menu) > Add-ons

In the left column, click Plugins. Note that disabled plugins cluster at the bottom of the list.

Sorry I just realized you are looking for old versions, not the current version. You may need to use a different browser for the site if those are "hard blocked" in Firefox (cannot be switched from "Never Activate" to another setting).