As the forum rules stipulate, you're supposed to tell us what operating system you use & details about your set up. I'll guess you're a windows user. My advice is:

1. Use your Add/Remove control panel to remove all versions of Java. Then install the "Offline" (specifically only this version) of Java 1.5 (take the JRE)

2. Delete your LW preferences as described here Point #2 & 3 in Fixes for Limewire (sample image included.)

3. Make sure your softw firewall is configured to allow LW, & that your modem/router has UPnP enabled; see the whole of this page Connection problems? Check here first! (click on link)

4. Then try opening LW.