I have always been able to connect to Limewire with my firewalls activated because Limewire is an exception to being blocked. However, I cannot connect enough to downlaod music. Can someone help me?

Sorry, but your post's confusing. Can you just clarify a bit?

You can't connect enough to download music...do you mean that your LW's connection to the network (green connection bars) has dropped off, or are you seeing files connecting for ages but never downloading (but connection to the network is ok)???

If you're not connected to the network, you need to give some details.
System details - help us to help you (click here)

If it's the files themselves not connecting...could be fake files that you're seeing. The threads below have more info & tips.
Fake files showing up in search results
How to find music (tips for video as well)

If every file (even old songs with 10 sources or less) gets stuck connecting, try this: Delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.