I found a great application called `gnome-main-menu` and quickly replaced the dual GNOME `gnome-panel` layout with a single panel. Yet, I'm not finding many ways to edit this menu. I can add and remove my "Favorite Application", but can't manipulate any other things, such as to change the "Computer" text or the information displayed under "Status". I checked, but `gconf-editor` didn't seem to have any answers.

Are you talking about this: http://en.opensuse.org/GNOME/Slab ?

It's not renown for it's configurable options, but then none of the various GNOME menus are all very hackable in my experience. There are some options in gconf under desktop > gnome > applications > main-menu.
As far as I know you can't modify the contents of the status section. There's a gconf option to hide it but that's all. As far as I know you can't modify the word 'Computer' either. Possibly something to do with what's gets displayed being language sensitive E.g. if you login with your language set to French then it says Ordinateur instead of Computer.