Perhaps a web browser popup-blocker blocked the download of Java.
Downloading & re-installing the "Offline" Java is no doubt an easier approach since you are not sure about the location of c:\Program Files\Java\jre6\bin\java. Try this link instead
What is the offline method for downloading and installing Java for a Windows computer? and choose the OFFLINE installer.
Before installing Java, right-click the Java installer & choose
Run as Administrator.
. This
is necessary if you wish to use LimeWire on Windows 7.