In rearranging the panel, I removed the Network Manager Applet. I tried to add it back, but it doesn't show up in the list (Add To Panel). I can start it up and see it as a running process (nm-applet), and I'm still connected to the internets, but I don't know how to get the panel icon back.
You have to add the Notification Area applet to the panel. The network manager will show up there.
System -> Preferences -> Startup Applications
Check "Network Manager"
If it's not in the list then add