Thanks for the reply.
I was able to resolve the problem late last night.
I had to uninstall the 1.7 java versions, reboot, install the 1.6.27 java version and used
Verify Java Version to verify that I really am running on 1.6.27. Then I reinstalled LimeWire and it worked.
FYI, Windows 7 automatically runs the Java exe's as administrator. It doesn't seem to matter whether I go through the extra step to right click or not.
Afterwards, LimeWire had trouble connecting, it was "connecting..." forever. But I used applied the connection fix you supplied in some other post on the forums and it was able to connect.
Regards,
Griff