First of all, LW is a Java based program and thus needs Java to run. You have to enable it (besides IE is much more vulnerable to attacks then Java IMO). Use FireFox instead.
Secondly, you should actually not use the Control panel>Remove Software function to uninstall LW. It is better to use START>Program>LimeWire>Uninstall.

I'd recommend you uninstalling the Java and rebooting. Then enable Java via the IE. I think it should be done via the Internet options (though I haven't use IE for qiute some time -I don't even have it installed).
After that reinstall Java using the JRE offline installer of the newest version which you can get here:
http://java.sun.com/j2se/1.5.0/download.jsp

Then reboot again and install LW. Then configure your Norton to allow LW access.

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"Never Argue With An Idiot. They Will Drag You Down To Their Level, Then Beat You With Experience"