Trouble with "Share Screen" and "Connect As" over the internet.

I have an AEBS, 3 MPB's, a MacMini, an iMac20, and an iMac27 all are running Mavericks 10.9.2.

All have File, Printer, and Screen Sharing turned on

One machine is giving me a problem when I select the computer name in Finder when attempting to "Share Screen" or "Connect As"over the internet. I am able to connect using either button when both machines are on my local network.

I am able to "Share Screen" with all the rest of the machines when sharing over the internet, but not able to "Connect As".

I've spent a considerable amount of time trying to resolve this issue but to no avail.

Help would be appreciated.

Regards.

Jim P.