AVChat needs a media server in order run, do you have a media server?
If you do, here's what you should do in order to see exactly why AVChat is not able to connect.
1) Is the connection string inserted correctly in your WordPress backend? Here's how it should look:
2) If the connection string is correct, you'll want to check if your media server is running on your VPS/cloud/dedicated/personal server.
A fast way to do this, is to go to : http://your-server-ip:5080 (if you're running Red5) or http://your-server-ip:8088 (if you're runnning Wowza).
Another way to do this is to use a port checker like http://www.yougetsignal.com/tools/open-ports/ and test your media server for incoming connections against port 1935.
If you can't access those pages or if the tool above reports the port as being closed it does not necessarily mean that the media server is not running, a firewall might prevent incoming connections to port 1935.
Thus the best way to check if the media server software is running is to connect to your server (SSH if your server is running Linux, or RDP if your server is running Windows) and check.
3) If you connected to the VPS/cloud/dedicated/personal server and the media server software is indeed running, you should check if a firewall is preventing incoming rtmp connections to your media server over port 1935. AVChat will connect using the 1935 port. This is the default port used by Red5, Wowza and FMS for rtmp connections. This is rarely the case.
4) Last, you'll want to check the media server logs. In there you should find the exact reason AVChat fails to connect to the media server. In Red5 you will find the Red5 log in red5_installation_folder/log/ under the name red5.log. You may also want to check AVChat's log, which is found in the same folder.
On Wowza, the logs are located in wowza_installation_folder/logs/