I'm not sure about my local network address ip and no I haven't tried a serial connection yet , excuse mr being naive but should I use the mini USB cable or connect via the LAN cable?
You won't be able to connect via LAN if you can't get to 192.168.1.77. Of course your LAN cable
should be connected, otherwise you certainly won't be able to see the Sheevaplug. The serial connection would allow you to verify that the plug is active, but if you are a beginner, may be more tricky than investigating your network setup.
On the network side of things, do you have a router or modem, how are they connected to your PC, and what is the O/S on your PC?
Under Windows, you can determine the IP addres sof your PC by typing
ipconfig at a command prompt (start / programs / accessories / command prompt)