Solze, we would need much more information about your particular network topology before we can answer the type of question you have here.
You stated that the PC is in the DMZ. What sits between that PC and the rest of your lan? Are there routers, switches, firewalls, etc? Have you tried doing a tracert to see if that gives you any clues? What about your event logs? Have you checked those? Is there a personal firewall on the PC that may be blocking pings? What device is your gateway? Is it a router, firewall, what? Is your network sub-netted, or just one big broadcast network? Do you have any network monitors in place to gather and analyze the overall network traffic on your LAN?