Do you have an internet connection open before you launch LimeWire? If not, try while you are already conencted to the internet.

Try downloading the latest version of the Java RunTime Environment from:

http://java.sun.com/j2se/1.4/download.html

Install it before re-installing the latest version of LimeWire which you will have just downloaded again (perhaps your download is corrupt).

Or, you can provide some more information about your system:
Windows version?
Java version?
Internet connection?
Firewall/router?
anti-virus software?
Anything else that might possibly be related. If you aren't sure what might be significant then include everything down to what type of taps you have on the kitchen sink.

{lots of people are running LimeWire without a problem under all versions of windows - something about your system is different to theirs - I can't tell what it is from here without a lot more information}

Mark