Most of these "class not found" errors are caused by a corrupted installation of Java on your system: Java cannot find its own runtime libraries.
The best advice is to reinstall Java: first uninstall it using the Windows control panel "Add/Remoe Program".
Then visit the official download page of the Java JRE :
http://java.sun.com/getjava/
Click on the download button at top. The install should start downloading a 9MB file, and the InstallShield installer will launch and cleanup your Java installation.
The installer will ask you if you want to enable support for Java in IE or Netscape. Check both options if you have both explorers.
The Sun Java engine works much better than the deprecated Microsoft VM for Java 1.1.3, that Microsoft will definitely abandon next year (Microsoft only publishes security updates, and is currently porting all its proprietary Windows integration classes to the Sun Java VM, and it should abandon its deprecated VM at the beginning of 2004, prefering to concentrate its efforts now in C# and .net, and integrating .net support classes in the standard Java2 platform).
Once complete, there is normally no need to reboot. The download page will immediately display a Java applet showing an animated cup of coffea.
To test the performance of Java 1.4, visit the Java showcase, notably the 3D animation demos. If these applets work correctly, then you can restart Limewire with the newly installed VM which will be automatically chosen if this is the default version selected with the standard Java selector control panel.