I'm having the same issue since yesterday and this morning (it's been approximately one month since the last time I was on LW.) "You are currently connecting to the network"...
I did recently have to replace out my cable modem, and after updating my Java to 1.6.0_03 last night I was finally able to connect, however, the time it took was several minutes. Has something changed in LW? In the past, LW would connect almost immediately. I have not made any other changes to the existing settings. I'm running Windows XP SP2, 4gb memory, 86gb remaining HD space, Symantec Antivirus, Windows Firewall with Limewire set as an exception, Time Warner Cable, and an Ambit cable modem (TW was not able to provide me any additional info on the type of cable modem). I did pass the Port 6346 test too. I do have another notebook in the house connecting remotely via wireless internet, however, that has never in the past interferred with my wired desktop.