Aside from wait? No idea (the connect buttons never worked for me for some reason so I refrain from using them).
Launch LW (after making sure you're connected to the net first of course...) and wait a little. It seems that the first time LW lauches, it's pretty slow (they say it's the same as with all Java apps) so it might take some time to initialize before trying to connect.

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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-