It sounds like you are using a buggy version of LW (probably 1.5). Version 1.6b works much better, but if you want to use 1.5, do this:

When the windows comes up looking for the "javaw.exe" file, it is looking for the file in the wrong place (more than likely C:\WINDOWS\SYSTEM).

Simply browse and find the file in C:\WINDOWS. When you click ok, LW should start up.

Be warned, though, that 1.5 is known to spontaneously close itself, crash, and/or refuse to connect. I would recommend downloading the newest available version from

http://www.limewire.com/index.jsp/download

Good luck! (To try to run 1.5, trust me; you'll need it)