despite the fact that it crashes the KERNEL32.DLL (which is a windows lib) I guess you have problems with the runtime environment. Since I'm sure you don't have a seperat JRE installed on your computer you are probably using the Virtual Machine coming with the limewire executable for windows. (say NO if something I gues here is not true).
In this case you should try to reinstall LimeWire (uninstall before doing the reinstall!) you might have to download the LimeWire Installer again.
there is a second way however. You might install the above mentioned JRE from sun. in this case LimeWire will use the JRE instead of the virtual machine... bla bla...
try the first way if it does not help get a JRE from here
http://java.sun.com/1.4/download.html

mahalo