What you can try do is the following, bear in mind ir n00b so dont shout me.
You have no access to router, either physical or logically.
You need to identify your external gateway IP address or addresses. Basically you need to find out what is your companies internet IP or IP's. You then need to PortScan those gateway IP's. Now it gets a litttle complex. If your IT dept is good they will disable ICMP packets and filter ping packets.
I would advise doing reconnaisance via a linux pc so that you can use NetCat(People with mullets in the states call it the swiss army knife). The Win32 port doesnt work that nicely. It has advanced options of determining host parameters and some other stuff. Use Netcat to find what your gateway can and cant allow. A head start would be trace routing.
Then if you find a port open you can do a few things. Either get it someway to work with your vnc or google 'fpipe' You can then redirect or craft packets in a direction to where you want 'em.
In my opinion, I would just go with a box of warm Spar donuts to the IT dept and ask them to forward VNC port to your work PC. IT guys feel so unappreciated in the corporate environment the donut trick will bowl them over.
My advice,
Peon