AOL needs to be running and connected to the internet before you run LimeWire.
If you run LimeWire before AOL is connected to the internet, LimeWire will not be able to connect until you dial in to the internet with AOL. Clicking the big red "Connect" button at the bottom of the screen should attempt to connect you.
If the button is green, then you are connected to the LimeWire Network (actually called Gnutella network). The numbers to the right of this button represent the amount of files and other users you have access to. A search will bring you no results if the button is red or it shows that you are not connected to any hosts.

Feel free to post again if needed. There's no such thing as a bad question here! :-)