Have you tried any of the fixes in the thread below? Start off by deleting LW's preferences folder & if that doesn't help, try the older version of Java, or try changing ports (details for all in thread below). Do these things before the other fixes in that thread.
If LW Will Not Connect

Have you been able to connect with older versions of LW? Did the connection problem start after installing the latest version?

If nothing helps, you could try the latest LW Beta verison & see whether that's any better ('get Beta' button on the right side of the main download page).
Lime Wire » Download LimeWire
Remember to use the offline installer...when you click on your download platform, cancel the dialog box which pops up. Now use the option to download the offline installer.