What version of Java are you using? Some people have had connection problems after updating to 1 6 0_01. Try this version. Use the JRE offline installer & remove your current Java version before you install this one.
Java SE Downloads - Previous Release - JDK 5

If that doesn't help, 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.

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