Realtek RTL8139 is for lan isn't it?
Change LW to manually connect not auto connect (LW's menu Tools>Options>Connection & untick option box & press both Apply & OK buttons.) Then go to File menu & choose connect. Wait up to an hour for LW to settle down. Any difference?
An hour does seem like a long time I know. After that, if still no success go here:
http://www3.limewire.com:6346/ & it should say your test page was a success. If not then we'll see what can be done.