Same issue in civi 4.7.3 and 4.7.8, on joomla 3.5.1. Payment Options shows up in Registration (Test Drive) and Registration (Live) but does not show up in front end, in the live site. I have another site using civi 4.6 and I have no problems there. Should show Paypal and Pay Later.
Forgive me if the question seems obvious but this sounds like what I had initially reported as a bug on JIRA in https://issues.civicrm.org/jira/browse/CRM-17214 but it turned out to be a slight change in behavior between versions.
Hope this helps!
There is a fix (work around). It is only needed for users on Joomla. And that is the java fix- Go to System Settings / Resource URLS. Change the path for CiviCRM Resource URL to be /administrator/components/com_civicrm/civicrm/