Please see the LimeWire FAQ

http://www.limewire.com/index.jsp/faqs#i12

A. The Java installer can occasionally freeze on some systems. While we (and InstallShield) are not sure precisely what is causing this problem, there is a potential work-around. Following the steps below may get your LimeWire up and running successfully.

When the installer freezes, DO NOT STOP THE INSTALL PROCESS and go to the Start>>Settings>>Control Panel window. From there, go to "Add/Remove Programs". If you see "Java 2 Runtime Environment Standard Edition v1.3.1" listed, then the Java installer has probably been installed successfully, and you should now continue to step 2. If you do not see "Java 2 Runtime Environment Standard Edition v1.3.1" listed in the Add/Remove Programs window, try downloading and installing the JRE directly from Sun at: http://java.sun.com/j2se/1.3/jre/download-windows.html. Once you have installed the JRE, then try running the LimeWire installer again.
Ok, so you have verified that the JRE is listed in the Add/Remove Programs window. You can now close the Add/Remove Programs window. Once you have closed it, press ctrl+alt+del on your keyboard. This will bring up a window that will be slightly different on Windows 95/98/ME than on Windows NT/2000. On Windows 95/98/ME, select the "Java(TM) 2 Runtime Environment, Standard Edition, v1.3.1 Setup" line and then press the "End Task" button. On Windows NT/2000, press the "Task Manager" button. Under the "Applications" tab, select the "Java(TM) 2 Runtime Environment, Standard Edition, v1.3.1 Setup" line and press the "End Task" button.
Close the Task Manager window. If everything worked correctly, the LimeWire installer on your desktop will have moved on to the next step. You should now be able to complete the LimeWire setup and run LimeWire.

Let me know if that helps,

Avi