Dare I suggest it but try Standalone Java solution & follow the link.

Post back to tell us how you go. If not good, then please supply your specifics about where you're connecting from: home, work, school, etc. ? And provide the specifics of your modem & router brand name & model number.

Oh & did you try trashing your LW prefs? This sometimes does the trick. They're found here: /Users/your_username/Library/Preferences/LimeWire & the folder/files name is .limewire
But keep in mind once you delete the prefs you'll need to reset your settings. So make a note of hem 1st!