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How to troubleshoot network issues:
First use ping to find out if your device is "alive". If it doesn't respond then it is either:
too busy to reply (this is bad)
blocking ping requests
or the ping request never reached the device or the response didn't make it back
Use traceroute to determine if the Internet connection to the device is ok. If the results show a lot of hops (like more than 20) or if the hops are showing delays (latency) of more than about 500 milliseconds (ms) then it's very possible your device is not responding because of Internet congestion, not because the device is down. If the traceroute results come back ok (i.e. traceroute dies at the last hop - at the device), then either the device is blocking ping (ICMP) or it's off.
Use port scan to see if the device is possibly responding on a different port. You can also port scan to check for possible security holes (open ports) in your firewall or use a free online firewall analyzer like Symantec Security Check, Sygate, or Hacker Whacker.
For more information on how to troubleshoot your Network, read this writeup by Bradley Mitchell or get this book by Joseph Sloan.