Hi All,
Thanx for all your advice, here is the latest update. I have updated Java to the latest available. Completely removed Limewire Version 4.10.9 and any older versions so that there is not a trace of them left. Restarted PC and Installed Version 4.10.9. Same problem still exists - that is: When Limewire is started up and there are unfinished downloads still waiting, it automatically connects the Internet, even when the Preferences say not to. Infact, it connects and continues the downloads when in the Menu it says "Disconnected". Other than this problem it works faultlessly.
Any further ideas would be nice!