After uninstalling, reinstalling, and trying different versions of Java, I finally found a solution that will work.
I wanted to write up the instructions so that others may benefit if they happen to stumble upon this thread through Google or some other searching apparatus.
1. Uninstall Symantec Endpoint Protection Manager using Add/Remove Programs.
2. Navigate to C:\Program Files\Symantec and look for "Symantec Endpoint Protection Manager" folder. If it exists, delete or rename it.
3. Go into Control Panel and open Java Control Panel. Under Temporary Internet Files, click "Settings" then click "Delete Files." Note that this will delete all Java applications (so use this step with caution).
4. Completely uninstall all versions of Java using Add/Remove Programs.
5. Download JavaRa (http://raproducts.org). After extracting, run JavaRa and select "Remove Older Versions." It should prompt you through the rest of the steps. You might also find it useful to click "Additional Tasks" to have it "Remove useless JRE Files," "Remove Startup Entry," "Remove Sun Download Manager," "Remove Java IE BHO," and "Remove Java Console Extension."
6. Reboot computer.
7. Install Java6u7 (You can find this off the internet if you search for it... Java 6 Update 7).
8. Go onto the Symantec Server (port 9090) and install the SEPM. It should now install and work as expected.
Hope this is useful to someone else!
Thanks to fieloer for pointing me in the right direction.