The OBi100/110 is a standalone device. The only role the OBiTALK Web Portal plays is remote configuration. The OBiTALK Web Portal doesn't relay star codes or interact with calls or facilitate anything other than remote configuration changes.
If you're having problems accessing the OBi via the OBiTALK Web Portal, you might consider setting:
System Management -> Device Admin -> Web Server -> Port : 8080
and forwarding port 8080 in your router to the OBi.
Then you can access the OBi remotely using the OBi's public (not LAN) IP address:8080 and not need to use the OBiTALK Web Portal. If your public IP address is dynamic and changes periodically, you should consider a free DynDNS account which will assign a hostname that's always current. Most routers support DynDNS updating.