I'm also having the same problem with my site. Just upgraded to the latest version. Same issues, Popup does not remove the welcome statement and does not show all the information below, including the send/close buttons. The Welcome Intro that is apparent when operator is online does not go away when operator is offline. See attached. Is this a CSS issue or Javascript issue?
The popup window has been completely re-designed and this issue has been resolved in JLive! Chat v3.7.0 which should be released any day now. Your desktop application will notify you when the new version is available for download.