java installs, but not found on drive or websites needing Java

I am unable to use certain websites such as loudtronix because of missing Java plug-in. I am using OSX 10.8.5. I installed JavaForOSX2013 that was downloaded from Apple. The installation appears to work, but when I go back to loudtronix, it still says "missing plug-in". I installed Java with the browser off, antivirus off (Sophos), and Firewall off, but no luck. I've made sure to reboot after installation. No Java icon shows up in "system preferences" and there doesn't seem to be any evidence of a java plugin when doing a search on my computer

I tried downloading the java.com version for OSX 7 update 40 but that does not download at all. I don't see any files in my download section and I do allow all software from all sites to be downloaded. Since no software appears, I DID NOT install the Java.com version.

I go to java.com for troubleshooting. It says I have an old version of Java, but when I verify the Java version, I get "missing plugin". I understand there is no Java installed on 10.8.4, so that's why I've spent 3 hours trying all combinations to get it to install or work using Apple's Java.

Is Java not installing or is the loudtronix website unable to recognize the Mac OSX Java? Why can't I find any evidence of Java on my computer (plugin, etc)? Are there any other versions of Java I can use that will work on websites like loudtronix?

Using Safari 6.05, Firefox 24.0. on brand new 27" iMac, OSX 10.8.5

I used to use 10.4.11 so I'm not familiar with all the features of 10.8.5.

Thanks--any help would be appreciated.