Find My iPhone app is not necessary to use on the iPhone. The purpose of the app is to help you locate someone elses iPhone. Find My iPhone has to be activated in iCloud. If your device is not showing up when logging into iCloud, then it must not be activated.
The reset that you did is not what is needed on your device. The wipe I was referring to would be the remote wipe in iCloud, however it cannot be accessed if you did not have iCloud signed in on the phone. This support document provides the procedures for restoring your phone, but without the computer and iCloud, you are not in good shape. http://support.apple.com/kb/ht1212
You could connect to another computer and restore the device, but that will delete all of your data. You will lose everything, but you will regain use of your device.
Message was edited by: ChrisJ4203