If you are dialing into AOL, you are definitely not connected to the Internet. You are connected to AOL, and AOL is not an Internet Service Provider. The closest anology is that you are dialing into a shopping mall that has it's own window into the Internet. What you are trying to do is somewhat like dialing into AOL and trying to use Netscape Navigator or MS Internet Explorer to browse the Internet. It won't work.

If there actually is a direct connection between your computer and the Internet (which is what any normal ISP provides), LimeWire is connected automatically, if automatic connect is enabled in the preferences. Otherwise, simply doing FILE > CONNECT will cause LimeWire to try and get connected.

Unfortunately, as an AOL subscriber, you can only gaze thru AOL's window into the Internet. You need to get a real connection to the Internet via a real ISP.