One of the first tasks you may want to try after configure your Azure VNET and adding VMs to it is to try to ping them from either another VM on the VNET or a client PC.

By default the ICMP protocol used by ping is turned off.  So you can’t ping your VM unless you allow the ICMP Protocol. To enable ICMP remote desktop into your VM and using the Windows Firewall with Advanced Security create a custom inbound rule. Choose the ICMP protocol and enable all inbound connections.  Depending upon whether you are sourcing your ping request from VMs within the same VNET or not will determine if you can ping the external IP or not from outside the VNET.