Thanks for the encouragement and suggestion.
What program are you currently using to ping your cable modem? What ISP do you use, and what cable modem do you use? I suspect that the "ping" you're program does is a different type - not using standard ICMP echo to do this.
Since you state "but since that server in not inside the network, is not reliable", I'm suspicious as to the ability to even access this information from your computer at all.
You should be able to ping 10.0.0.0 with Ping Plotter, although I don't (and never have had) have a device that would respond to that IP, so I'm not sure.
Let me know more details about your situation / hardware / software and I'll see if we have anything that can help with this.