Hello Rose
You don't say whether you can connect to the internet or just that limewire will not connect.

If it is the the internet then use the AOl dialler "one click fixes"
I would suggest you repair your ACS ( it's on the list )
if that doesn't work then use the RE-BUILD ADAPTER/ACS

I note your using Zone Alarm.... whilst this is a excellent product , it has been known to cause issues with connectivity and AOL 9.0. If you are an AOL consumer you can get a free copy of mcafee's firewall which to date i have had no issues with.

The other possibility is that anti-P2P companies are flooding your computer with connection attempts. The only defense I have used and know of is PEERGUARDIAN which you run and update before using LW. I will let you do your own research on that one.... there are others more knowledgable than me about such things.

Best of luck to you..... hope i have at least put you in the right direction.