Dump the icon into the trash, go to the Home directory, enter the Library, find the Preferences folder and the LW folder inside that and dump that too.
Go back to www.limewire.com and redld the latest version of LW. Reinstall. See if it works.

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iMac G4 OSX 10.3.9
RAM 256MB
LW 4.10.5 Basic
ADSL anything from 3 to 8Mbps/around 1024kbps

"Raise your can of Beer on high
And seal your fate forever
Our best years have passed us by
The Golden Age Of Leather"
-Blue Öyster Cult-