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You should mirror the router switch port and put Wireshark on it using a laptop, etc. That will tell you exactly what traffic is going in/out and in what quantity. monitor session 1 int f0/1 (ingress/egress port) bothmonitor session 1 destination in...
What does this command show?sh proc mem Even if the memory is full, some packets should be able to ping something outside your network if you can ping something inside of it. If it wasn't able to, my thought is that it would crash and dump eventuall...