Internet troubleshooting

Hi to everyone out there I have a issue and would need a help, firstly I have a Cisco management which served as the main router to my network and does the dhcp for my local network and serves as my border router to my isp. When I ping any local machine on my network the ping reply is successful but I try ping my router the reply is fifty percent with this my internet is fluctuating can someone help me here
 
Certainly interesting that some work and some don't.
Almost ALL routers give you a control to enable/disable "Respond to ping from the Internet" side. It is thought that not responding is a better choice as ping is used to find systems that can then be further probed for implanting a virus (there are other techniques too however).

I've never seen a ping from that LAN side be configurable NOR fail to work either unless there's a real Source connection issue.

Also never possessed a Cisco router, so can't be sure what does/doesn't work here.

BUT; is this a real problem that demos some pc issues or just oh my, how interesting ..... ?
 
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