Using Windows Server 2012 I have seen a weird issue with the network adapter several times using mainly Hyper-V and VMWare as hypervisors and the problem server being a virtual machine guest.
When you set a static IP and DNS your server may fail to ping outside its LAN. You check and double check the settings and you have all the correct DNS subnet and Gateway Settings, yet you cannot ping a simple website such as Google.
When I check the routing table on the server I notice a persistent route for 0.0.0.0 mask 0.0.0.0 via the local IP address of the server. I also noticed another non persistent route for 0.0.0.0 mask 0.0.0.0 ON-LINK via gateway ip address of the server.
These two routes are your problem.
The best way I have found to resolve this issue is to run this command in elevated command prompt
route delete 0.0.0.0
This will remove all default routes from the routing table. Then just add a persistent route for 0.0.0.0 to route via the default gateway address like this
route add 0.0.0.0 mask 0.0.0.0 126.96.36.199 /p
Your server should now start behaving properly