If you're accessing VNC from remote locations you do NOT want to be doing so directly. VNC has absolutely no security whatsoever, so all your traffic could easily be monitored.
What you do want to do is tunnel the VNC port through an SSH connection. There are loads of threads here on how to do this.
I have a VNC server running on my Linux server at home (tcp 5900). I can access it from various remote sites, but not from work. I can however access my FTP site (same system) from work.
Just be aware that your system admins at work may take a very dim view of you accessing a home computer from work, and given your description, it seems likely that they are actively trying to prevent people from doing what you're trying to do. Depending on where you work, circumventing network security can be grounds for termination.