I loaded the client on my server, it appeares to have gotten my IP address, but if I ping the address from outside of the office it times out. I am also trying to connect to my server using terminal services but the connection failss.

Both of your hostnames map to IP address 24.191.187.78 and it was updated about 20 minutes ago. Please let us know if this is not the correct IP address. If this is the correct IP address, could you please try connecting directly using IP address?

If the connection cannot be made using IP address either, could you please make sure that you have opened the necessary ports in the router to allow terminal services? You may use this port check tool at https://www.dynu.com/NetworkTools/PortCheck to check if the ports have been open or not.

Please note that ping is not always guaranteed to work since some routers don't respond to ICMP packets.