Who doesn’t know it: the ping feature!
Of course you can still execute any of the good old commands via the command line tool (cmd.exe):
ping, hostname, ipcondig, nslookup, net, netstat, netsh, pathping, nbtstat, route, tracert, getmac

The ping tool allows you to find out if you can establish a connection with a certain IP address or domain:
Windows 7 Ping Tool

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But what if you are receiving a “general failure” ?

C:\>ping 192.168.1.1

Pinging 192.168.1.1 with 32 bytes of data:

General failure.
General failure.
General failure.
General failure.

What then? Well, most of the time your firewall is simply blocking access to the internet (as it is supposed to)!
Solution: Try to disable your firewall and you should no longer receive a general failure.

Especially the norton firewall is blocking basically anything. You shouldn’t have any problems to execute the ping command with a AVG or the built-in Windows firewall.