Hi,
Yes, you can do it with Unity Networking... I strongly discourage you to do so... what kind of server are you going to run and who's going to maintain the server? With Photon Cloud, there is no server, it's done for you and for your needs, you only need basic communication from what I can see.
If you are in control of both pc, then you may be able to get away with Unity networking and without a server ( peer to peer connection on a same network).
Could you tell us more about the contact of this? Maybe a dedicated server is required, but we need more infos before stating this.
Have you tried the various samples on Unity networking do they work on your machine setup?
Bye,
Jean