The answer is going to make a difference in how you will have to troubleshoot the problem.
For example, if local name resolution works but Internet name resolution does not, the problem may lie with one of your ISP's DNS servers.
DNS is one of the most essential services on any Windows network.
Active Directory can't function without DNS, and it's is also used by any number of other network functions.
Even though many DNS servers use root hints for Internet name resolution, some use forwarders to link to an ISP's DNS server.
And if the ISP's DNS server goes down, Internet name resolution will cease to function as the entries in the resolver cache expire.If you can ping the host by IP address but not by name, check your DNS server to make sure that a Host (A) record exists for the host.Without a Host (A) record, the DNS server will be unable to resolve the host's name.If so, the problem could be related to a router failure or a DHCP configuration error.Organizations hosting high demand Web servers sometimes try to distribute the workload across multiple identical Web servers by using a load balancing technique called DNS Round Robin.If name resolutions are failing on your local network, try pinging some of the servers on your network. This will confirm that connectivity to the server is working.Next, try pinging by computer name and by the server's fully qualified domain name.The result is intermittent connectivity problems to the load-balanced resource.If you determine that local name resolution requests are working but Internet requests are failing, check to see whether your DNS server uses forwarders.One of the handiest tools for troubleshooting DNS failures is the NSLOOKUP command, which you can access from a Windows Command Prompt window.Simply type followed by the name of the host for which you want to test the name resolution.