Depends where you are saving your downloads to. By default they are saved to this location: C:\Documents and Settings\"your account name"\Shared. You can check by going to LW's menu bar, Tools>Options>Saving to see the location.
If you are saving them there, then removing the LW prefs folder or LW program will make no difference. Just next time you open LW, make sure you choose the same location, well it is the default location anyway.

It might be a pain, but try the offline Java version first; ie: removing other versions, then installing Offline version.

If all that fails, then uninstall LW. Then use the suggested version if all else fails.