So in Server Core the built-in Windows firewall comes on by default. You can choose to disable it completely to get all the networking components working by using this NETSH command,

netsh firewall set opmode disable

You can use the enable switch to turn it back on. However, completely disabling it may be a bad idea, and you should choose the following commands to specifically open up gates for certian ports and applications. For example to open up port 3389 for RDP use,

netsh firewall set portopening TCP 3389 "AnyNameHereSuchasRDP"

or

netsh firewall set allowedprogram FullPathToExecutable name=AnyNameHere

Note that above commands should be entered in one line, and are overlapped due to the page format in this post.

For more information on advanced firewall functionalty, please go here.