If HQ Client/HQ Server connection is not working, first make sure that port forwarding is enabled for the PC running HQ Server for port 34200.
Next run http://www.myipaddress.com on the PC running HQ Server to determine Internet address for the store. Other IP address appear to be showing something else entirely.
Ping that address from the remote store location to confirm it is accessible.
Next try this trick to test the port access for HQ Client connection (normally 34200).
From a command prompt type: telnet <IP address or name of machine> <port>
Example: telnet 188.8.131.52 34200
If you get a connection error, then the computer is not listening on that port.
If you get a blank screen, then this indicates that the connection has been made, so the computer is listening on that port.