The panel settings are stored in the .gconf/apps/panel folder in your home directory. Of course beginning with the "." it's a hidden file, you will have to enable viewing hidden folders to work with it in nautilus.
As far as restoring the default without a backup, you might could try booting a live cd and copying the folder above mentioned directory over to your machine. That should set your desktop back to the default.
Moving forward, I would suggest making a backup of that folder or adding it to your existing backup strategy... (you do have a backup in place don't you?)
The applet you are looking for is called the indicator applet