Can access server from outside network but not inside

I have a server with a public site that is accessible without any issues. The problem is that the server is not reachable via ping (ICMP is enabled and Win FW is off) by hostname or IP and we cannot map drives to it.

I can RDP into the system and I have verified the routing table with its backup server and made sure all routes (even persistent) are identical (save the local IP address difference).

Any help is appreciated.