I would like to know if this is common due to serer issues or whatever, or if its my internet/computer thats the problem.
Most likely the former. The servers took a pounding today, and were on and off. I would say wait a few days to start blaming your ISP/Network/etc.
One of the things you can do that may help is to use the ImpulseReactorOptions.exe application in your Demigod\bin directory. This will limit the number of ports that the Multiplayer connection server uses for you, and allows you to forward that range in your router (as opposed to the huge 6100-6200 block). By default I believe it's 6112-6132, and can be changed in case of multiple machines needing to be connected on the same LAN (port forwarding shouldn't allow overlaps, and most routers will not allow such a configuration)