You router is almost certainly set up to stop this kind of connection being made.
First I think you need to configure your firewall to allow connections to the ports than VNC uses - 5900 and also 5800 for some functions.
Then to solve the IP problem I think you need to use a facility called "port forwarding" - something which I have no experience with. You'll need to look in your router manual to find out how to do this. The basic idea is that attempts to connect to a specific port at the IP address given to you by your ISP (which belongs to the router) get forwarded to a PC behind the firewall.