As you are using a router it is probably configured as a DHCP server, most are by default, you need to set evox to static=no in the network set up then save the settings and reboot. The xbox should then get an ip assigned. To ping just open a command prompt on your PC, in Win XP just go to RUN and type CMD then hit enter. In the dos prompt type ping leave a space and the type your xbox IP, so if your xbox IP was 192.168.1.2 you would type ping 192.168.1.2 if the network is working you will get 4 replys if not you will get timed out. While in the command prompt type ipconfig /all and post the result this will help to work out your setup.
Ping is just to verify connectivity it does nothing to establish a link.