I ran into this problem with a windows server I had on a static IP. When I connected VPN, the only computers I could ping using the FQDN were the ones using DHCP. The static machines timed out.
What you need to do is go into the Server Manager>Hostnames and Addresses tab. There you need to setup your computer hostnames with the local IPs. If you were using the DHCP server, these entries would be automatically added to the DNS server. Since you're using static IPs, you'll need to add them manually.