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when ping is not performed either that address is denies or servers is down if ping is denied only then other functinality will work remote accessing through browzing etc if server is down then or connectivty is down then prtg or other tools will informed you in this condition you will login munuly to that devices becuse in this condition your telnet ssh is not working
it might be the problem with inter vlan configuration with the router, check and make sure configure it properly so it can meet all the requirements with vlans