First see what problems I was having to see if this will apply to you.
Diagnose:
Open Firefox and open the pop-up chat window. Do not hit continue yet.
In Firefox open "Tools" then "Error Console". Keep it visible so you can watch for errors as they happen.
Enter a name in the pop-up window and hit "Continue"
In the Firefox Error Console you may see...
Error: invalid flag after regular expressionSource File:
*your-domain-name**/media/system/js/mootools.jsLine: 81, Column: 11Source Code:<b>Warning</b>:
fsockopen() [<a href='function.fsockopen'>function.fsockopen</a>]: unable to
connect to **your-ip-address**:5890 (Connection refused) in
<b>/**path-of-server**/components/com_livechat/models/popup.php</b>
on line <b>67</b><br />
It means the port fsocketopen is trying to use is being blocked.
Problem: GoDaddy limits PHP fsocketopen to ports 80 and 443 only.
Solution: Delete the old key from the server software. Set the server software to use either port 80 or 443. Delete and regenerate a new key in JLiveChat settings. Download and import the newly generated key into the server software.
If now you see the Connecting... message in the pop-up but it still does not connect then try the following.
Edit the components/com_livechat/models/popup.php file. Please make a backup of the original.
In popup.php look for the function "sendMessage" about 4 lines further down you will see "10". This is the timeout in seconds for the client to reach the server. I had to change it to "20" seconds.
Good Luck and thanks to "Support" for helping me figure this out.