I've finally gotten eclipse installed on my 14.04 machine so that it launches from a new terminal with an eclipse.desktop file. I can drag it onto the launcher and when I click it everything works!
Except when I close eclipse later, shut down, boot back up, and the eclipse.desktop file is no longer on the launcher. Instead is an icon from a previous installation of eclipse that leads nowhere.
So there are two issues here, how to get rid of the icon from the previous installation, and how to get the .desktop file to stay on the launcher.