A friend had a computer with the following symptoms:
ping cnn.com(or for any other domain) gave the message
Ping: cannot resolve cnn.com: Unknown host
ping 126.96.36.199(or for any other IP) gave the message
Ping: sendto: Host is down
We were both on the same network (Oxford University's 'OWL', which you have to use VPN with to visit non-Oxford sites and avoid getting redirected to an Oxford page asking you to log on. So on my Mac I looked at [System Preferences > Network > Advanced button > DNS] and copied the 'DNS Server' and 'Search Domain' that showed there when I connected to OWL (it seemed they were auto-detected). I then added them to the same place on my friend's computer, which had other DNS servers and no Search Domain. That fixed things.
Why was this? In general, how can I diagnose problems like 1 & 2 above.