I don't typically go to a specific page to test my connectivity. I go straight to whatever task I set out to do, then if that doesn't work, I do the following:
1. Fire up Terminal
2. Check loopback
$ ping localhost
3. Identify default gateway
$ netstat -nr | grep '^default'
4. Ping whatever gateway I find
$ ping 172.20.1.254
5. Try a known good IP address
$ ping 4.2.2.2
6. Check to see if the resolver is working (get root servers)
$ dig
7. Check to see if I can resolve specific hostnames (try a known good one first)
$ dig google.com
8. Check the specific hostname I'm trying to reach (but failed)
$ dig bradlanders.com
9. Try a name server other than the one I'm using
$ dig @4.2.2.2 bradlanders.com
10. Test IP routing to the destination IP
$ mtr 69.163.164.23
10. Assuming each of these passes, you can safely say the target service is down
Each successive step is taken only if the preceding fails.