Have you tried the deleting of LW preferences folder trick? Backing up your LW preferences downloads file at same time. Also obtain a new LPE connection fix for fresh connection data. It's been updated several times recently.

Java 6 should be fine. I connected well with it a few days ago on Windows whilst testing 3 versions of LW 4. My LPE Windows and Mac also connect fine.

If you have not used LW 5 in 30 or more days you will definitely need fresh connection data because LW will auto-delete it otherwise.

If you are using Vista, Windows 7 or later, then you may need to reset the Java to be running in Administrator mode by finding the Java.exe file and getting its properties and set to run as admin using there instructions. For some strange reason, this seems to have a huge impact on connecting if using the later Windows versions. If you are not sure how to do, you could always re-install the 'Offline' Java 1.6. Download the file, right-click the installer and choose to 'Run as Administrator'.
Direct Java 1.6_update 35 'Offline' download link

- Setting Java installer (and LW) to Run as Administrator.