Finder->GO->"Connect to Server" is not there -⌘K doesn't activate either

Nope, that's a new one to me.

You don't have Simple Finder or something like that turned on? I really don't know if that will remove that menu item, but I suppose it could.

Download any odd programs that modify the Finder in any way?

If you actually are living in a very warm place, you can always go to the Terminal app and use the command line interface until we sort this out.
Type 'man mount_afp' to find out how to mount from and afp server (apple) or 'man mount_smbfs' for a windows smb/cifs server. There are other options, try 'man mount' and scroll to the SEE ALSO section for the various file system shares you can mount from the CLI. Those will bring up the manual pages for the commands so you can see what to do to get a share mounted.

I'll poke around in the preferences and see if I can discover any settings that might have it confused.

Ok, I've got another method to try to see if the networking works. You need to know the address of a share you want to connect to.

Open Script Editor and enter this line into the editor window with your appropriate address, then click the run button. It should start the connection process if it is working still.

open location "afp://shareIPaddress/sharename" with error reporting

It it is a Windows share, you could also use:
open location "smb://shareIPaddress/sharenem" with error reporting
I'm not sure if you need Windows Sharing enabled in the Sharing preference pane to access a windows share--I think it is only for a windows share to access your mac.