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The problem is most likely with your network card and/or it's drivers. Try a different network adaptor, even a USB WiFi dongle will do. If that's not possible, try a different PC. Borrow a laptop from a friend/colleague/relative. Alternatively try a smartphone or tablet? If you are on Android, iOS or Windows Phone, there are free apps available to do pings, tracerts and other networking tools.
some stats.Ping statistics for 10.0.0.2:
Packets: Sent = 361, Received = 361, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 0ms, Maximum = 15ms, Average = 0ms